DETAILED ACTION
This action is responsive to claims filed 02/03/2023.
Claims 1–20 are pending for examination.
Notice of Pre-AIA or AIA Status
The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA .
Information Disclosure Statement
The information disclosure statement (IDS) submitted on 06/27/2025 is in compliance with the provisions of 37 CFR 1.97. Accordingly, the information disclosure statement is being considered and attached by the examiner.
Drawings
The drawings are objected to because “The photographs must be of sufficient quality so that all details in the photographs are reproducible in the printed patent.” See MPEP 608.02.V(b). Specifically, the figures are blurry and not legible.
Corrected drawing sheets in compliance with 37 CFR 1.121(d) are required in reply to the Office action to avoid abandonment of the application. Any amended replacement drawing sheet should include all of the figures appearing on the immediate prior version of the sheet, even if only one figure is being amended. The figure or figure number of an amended drawing should not be labeled as “amended.” If a drawing figure is to be canceled, the appropriate figure must be removed from the replacement sheet, and where necessary, the remaining figures must be renumbered and appropriate changes made to the brief description of the several views of the drawings for consistency. Additional replacement sheets may be necessary to show the renumbering of the remaining figures. Each drawing sheet submitted after the filing date of an application must be labeled in the top margin as either “Replacement Sheet” or “New Sheet” pursuant to 37 CFR 1.121(d). If the changes are not accepted by the examiner, the applicant will be notified and informed of any required corrective action in the next Office action. The objection to the drawings will not be held in abeyance.
Specification
The specification is objected to for informalities.
The title of the invention is not descriptive. A new title is required that is clearly indicative of the invention to which the claims are directed.
Appropriate correction is required.
Claim Rejections - 35 USC § 112
The following is a quotation of 35 U.S.C. 112(b):
(b) CONCLUSION.—The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the inventor or a joint inventor regards as the invention.
Claims 1–19 are rejected under 35 U.S.C. 112(b) as being indefinite for failing to particularly point out and distinctly claim the subject matter which the inventor or a joint inventor regards as the invention.
Regarding claims 1–2, 9–10, and 15–16, the claims include acronyms with no definition for the meaning of the acronym (i.e., CLF V). It is unclear as to the exact meaning of those acronyms and, therefore, indefinite. In the interest of compact prosecution, examiner is construing the acronyms as follows: “control Lyapunov function (CLF)”.
Regarding claims 1, 9, and 15, the claims recite “has not decreased sufficiently,” which is a subjective term because there is no objective measure for the scope of the term provided in the specification. See MPEP § 2173.05(b)IV. Therefore, the limitation is indefinite. In the interest of compact prosecution, examiner is construing the limitation to mean “has not decreased.”
Regarding claims 3–8, 11–14, and 17–19, each of these claims depends from a claim rejected under §112(b) and necessarily includes all the limitations of the claims from which they depend, respectively. Therefore, claims 3–8, 11–14, and 17–19 are also rejected under §112(b) because of their dependency.
The following is a quotation of 35 U.S.C. 112(d):
(d) REFERENCE IN DEPENDENT FORMS.—Subject to subsection (e), a claim in dependent form shall contain a reference to a claim previously set forth and then specify a further limitation of the subject matter claimed. A claim in dependent form shall be construed to incorporate by reference all the limitations of the claim to which it refers.
Claim 14 is rejected under 35 U.S.C. 112(d) as being of improper dependent form for failing to further limit the subject matter of the claim upon which it depends. Claim 14 recites “The method for modeling a device or process according to claim 9,” and it includes 3 sets of equations. However, claim 14 does not include any instructions or application of the equations. Therefore, claim 14 does not further limit claim 9 and is an improper dependent claim. In the interest of compact prosecution, examiner is construing the claim to be equivalent to claim 6 i.e., “wherein step d3) includes: advancing to (z(k + 1), x(k + 1)) using h_k^0 and
PNG
media_image1.png
185
454
media_image1.png
Greyscale
”
Appropriate correction is required.
Claim Rejections - 35 USC § 101
35 U.S.C. 101 reads as follows:
Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title
Claims 1–20 are rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more.
Regarding Claim 1:
Step 1 — Is the claim to a process, machine, manufacture, or composition of matter?
Yes, claim 1 is directed to a method i.e., a process.
Step 2A — Prong 1 Does the claim recite an abstract idea, law of nature, or natural phenomenon?
Yes, the claim recites an abstract idea.
“the accelerated optimization method comprising: a) a user choosing a CLF V convergence condition”
“b) initializing the accelerated optimization method according to
λ
x
0
= -αxL(1,
λ
s
0
,x0), s0 = e(x0) and setting k = 0;
c) computing Vk = V(z(k))
d) while stopping conditions are not met do;
d1) generate ζ(k);
d2) compute
h
k
0
;
d3) advance to (z(k + 1), x(k + 1)) using
h
k
0
d4) compute Vk + 1 = V(z(k + 1))
d5) while Vk + 1 has not decreased sufficiently do: d4a) backtrack (z(k + 1), x(k + 1)) along ζ(k);
recompute Vk + 1
d6) end while; and
d7) update k [Wingdings font/0xDF] k + 1; and
e) end while”
These limitations, under their broadest reasonable interpretation, cover mathematical concepts (including mathematical relationships, mathematical formulas or equations, mathematical calculations) and mental processes, concepts performed in the human mind (including an observation, evaluation, judgment, opinion). See MPEP 2106.04(a)(2). With regard to the mathematical concepts, in particular, the above initialization, computing, and updating processes all recite mathematical relationships, formulas, or equations. With regard to the mental processes, in particular, with the aid of pen and paper, a human can decide which CLF V convergence condition to choose. Furthermore, with the aid of pen and paper, a human can initialize an optimization problem (i.e., compute equations).
Step 2A — Prong 2 — Does the claim recite additional elements that integrate the judicial exception into a practical application?
No, there are no additional elements that integrate the judicial exception into a practical application. The additional elements:
“A method for processing digital representations of a group of objects and identifying within the group of objects a target object” — This limitation is reciting only the idea of a solution or outcome i.e., the claim fails to recite details of how a solution to a problem is accomplished such that it amounts no more than mere instructions to apply. See MPEP 2106.05(f); See also Electric Power Group, LLC v. Alstom, S.A., 830 F.3d 1350, 1356, 119 USPQ2d 1739 (Fed. Cir. 2016).
“the method including the execution of an accelerated optimization method to identify the target object within the digital representations of the group of objects” — This limitation is reciting only the idea of a solution or outcome i.e., the claim fails to recite details of how a solution to a problem is accomplished such that it amounts no more than mere instructions to apply. See MPEP 2106.05(f); See also Electric Power Group, LLC v. Alstom, S.A., 830 F.3d 1350, 1356, 119 USPQ2d 1739 (Fed. Cir. 2016).
Step 2B — Does the claim recite additional elements that amount to significantly more than the judicial exception?
No, there are no additional elements that amount to significantly more than the judicial exception.
Regarding Claim 2:
Step 1 — Is the claim to a process, machine, manufacture, or composition of matter?
Yes, claim 2 depends from claim 1 (see analysis of claim 1 above) which is directed to a method i.e., a process.
Step 2A — Prong 1 Does the claim recite an abstract idea, law of nature, or natural phenomenon?
Yes, the claim recites an abstract idea.
“wherein step a) of the accelerated optimization method includes: a user choosing a CLF V convergence condition and the parameters associated with a Problem (P) or (P*)”
“wherein step d1) includes generating ζ(k) by solving Problem (P*)( or (P))”
These limitations, under their broadest reasonable interpretation, cover mathematical concepts (including mathematical relationships, mathematical formulas or equations, mathematical calculations) and mental processes, concepts performed in the human mind (including an observation, evaluation, judgment, opinion). See MPEP 2106.04(a)(2). With regard to the mathematical concepts, in particular, the above includes generating an answer by solving a mathematical problem which recites mathematical relationships, formulas, or equations. With regard to the mental processes, in particular, with the aid of pen and paper, a human can choose a convergence condition and associated parameters.
Step 2A — Prong 2 — Does the claim recite additional elements that integrate the judicial exception into a practical application?
No, there are no additional elements that integrate the judicial exception into a practical application.
Step 2B — Does the claim recite additional elements that amount to significantly more than the judicial exception?
No, there are no additional elements that amount to significantly more than the judicial exception.
Regarding Claim 3:
Step 1 — Is the claim to a process, machine, manufacture, or composition of matter?
Yes, claim 3 depends from claim 1 (see analysis of claim 1 above) which is directed to a method i.e., a process.
Step 2A — Prong 1 Does the claim recite an abstract idea, law of nature, or natural phenomenon?
Yes, the claim recites an abstract idea.
“wherein step d2) includes: computing h_k^0 using, M_1(k) [h_k^BL^X] + h_k^BLM_2(k)X = b_k, where M_1(k), M_2(k) and b_k are matrices (of appropriate dimensions) that depend on the known values of iterates of at point k, and X is a variable that comprises za(k + 1), ψ_ λ_x, ψ_ λ_y, ψ_ λ_s, ψ_ v, ψ_s and ψ_ x, the known values of iterates given by:
PNG
media_image2.png
204
494
media_image2.png
Greyscale
”
These limitations, under their broadest reasonable interpretation, cover mathematical concepts (including mathematical relationships, mathematical formulas or equations, mathematical calculations) and mental processes, concepts performed in the human mind (including an observation, evaluation, judgment, opinion). See MPEP 2106.04(a)(2). With regard to the mathematical concepts, in particular, the above includes generating an answer by solving a mathematical problem which recites mathematical relationships, formulas, or equations. With regard to the mental processes, in particular, with the aid of pen and paper, a human can choose a convergence condition and associated parameters. Furthermore, with the aid of pen and paper, a human can compute equations.
Step 2A — Prong 2 — Does the claim recite additional elements that integrate the judicial exception into a practical application?
No, there are no additional elements that integrate the judicial exception into a practical application. The additional elements:
“the method including the execution of an accelerated optimization method to identify the target object within the digital representations of the group of objects” — This limitation is reciting only the idea of a solution or outcome i.e., the claim fails to recite details of how a solution to a problem is accomplished such that it amounts no more than mere instructions to apply. See MPEP 2106.05(f); See also Electric Power Group, LLC v. Alstom, S.A., 830 F.3d 1350, 1356, 119 USPQ2d 1739 (Fed. Cir. 2016).
Step 2B — Does the claim recite additional elements that amount to significantly more than the judicial exception?
No, there are no additional elements that amount to significantly more than the judicial exception.
Regarding Claim 4:
Step 1 — Is the claim to a process, machine, manufacture, or composition of matter?
Yes, claim 4 depends from claim 1 (see analysis of claim 1 above) which is directed to a method i.e., a process.
Step 2A — Prong 1 Does the claim recite an abstract idea, law of nature, or natural phenomenon?
Yes, the claim recites an abstract idea.
“wherein step d2) includes: computing h_k^0 using,
PNG
media_image3.png
389
545
media_image3.png
Greyscale
”
These limitations, under their broadest reasonable interpretation, cover mathematical concepts (including mathematical relationships, mathematical formulas or equations, mathematical calculations) and mental processes, concepts performed in the human mind (including an observation, evaluation, judgment, opinion). See MPEP 2106.04(a)(2). With regard to the mathematical concepts, in particular, the above includes computing a mathematical problem which recites mathematical relationships, formulas, or equations. With regard to the mental processes, in particular, with the aid of pen and paper, a human can compute equations.
Step 2A — Prong 2 — Does the claim recite additional elements that integrate the judicial exception into a practical application?
No, there are no additional elements that integrate the judicial exception into a practical application.
Step 2B — Does the claim recite additional elements that amount to significantly more than the judicial exception?
No, there are no additional elements that amount to significantly more than the judicial exception.
Regarding Claim 5:
Step 1 — Is the claim to a process, machine, manufacture, or composition of matter?
Yes, claim 5 depends from claim 1 (see analysis of claim 1 above) which is directed to a method i.e., a process.
Step 2A — Prong 1 Does the claim recite an abstract idea, law of nature, or natural phenomenon?
Yes, the claim recites an abstract idea.
“wherein step d2) includes: computing h_k^0 using,
PNG
media_image4.png
68
200
media_image4.png
Greyscale
”
These limitations, under their broadest reasonable interpretation, cover mathematical concepts (including mathematical relationships, mathematical formulas or equations, mathematical calculations) and mental processes, concepts performed in the human mind (including an observation, evaluation, judgment, opinion). See MPEP 2106.04(a)(2). With regard to the mathematical concepts, in particular, the above includes computing a mathematical problem which recites mathematical relationships, formulas, or equations. With regard to the mental processes, in particular, with the aid of pen and paper, a human can compute equations.
Step 2A — Prong 2 — Does the claim recite additional elements that integrate the judicial exception into a practical application?
No, there are no additional elements that integrate the judicial exception into a practical application.
Step 2B — Does the claim recite additional elements that amount to significantly more than the judicial exception?
No, there are no additional elements that amount to significantly more than the judicial exception.
Regarding Claim 6:
Step 1 — Is the claim to a process, machine, manufacture, or composition of matter?
Yes, claim 6 depends from claim 1 (see analysis of claim 1 above) which is directed to a method i.e., a process.
Step 2A — Prong 1 Does the claim recite an abstract idea, law of nature, or natural phenomenon?
Yes, the claim recites an abstract idea.
“wherein step d3) includes: advancing to (z(k + 1), x(k + 1)) using h_k^0 and
PNG
media_image1.png
185
454
media_image1.png
Greyscale
”
These limitations, under their broadest reasonable interpretation, cover mathematical concepts (including mathematical relationships, mathematical formulas or equations, mathematical calculations) and mental processes, concepts performed in the human mind (including an observation, evaluation, judgment, opinion). See MPEP 2106.04(a)(2). With regard to the mathematical concepts, in particular, the above includes computing a mathematical problem which recites mathematical relationships, formulas, or equations. With regard to the mental processes, in particular, with the aid of pen and paper, a human can compute equations.
Step 2A — Prong 2 — Does the claim recite additional elements that integrate the judicial exception into a practical application?
No, there are no additional elements that integrate the judicial exception into a practical application.
Step 2B — Does the claim recite additional elements that amount to significantly more than the judicial exception?
No, there are no additional elements that amount to significantly more than the judicial exception.
Regarding claim 7:
The claim is rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more. The claim is dependent on claim 1 which included an abstract idea (see rejection for claim 1 above). This claim merely recites a further limitation on the digital representations of a group of objects limitation which is directed to mere instructions to apply the abstract idea. The additional limitation:
“wherein the digital representations of a group of objects includes a plurality of object pixel images and the target object is a pixel image of the target image” — This limitation is directed to the field of use (see MPEP 2106.05(h)) as it merely limiting the fields of the group of objects to pixel images.
Thus, the judicial exception is not integrated into a practical application (see MPEP 2106.04(d)I.), failing Step 2A Prong 2. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception under step 2B.
Regarding claim 8:
The claim is rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more. The claim is dependent on claim 1 which included an abstract idea (see rejection for claim 1 above). This claim merely recites a further limitation on the digital representations of a group of objects limitation which is directed to mere instructions to apply the abstract idea. The additional limitation:
“wherein the digital representations of a group of objects includes a plurality of objects associated with characteristics of a device or process and the target object is a target object associated with a target characteristic of the device or process” — This limitation is directed to the field of use (see MPEP 2106.05(h)) as it merely limiting the fields of the group of objects to those associated with characteristics of a device or process.
Thus, the judicial exception is not integrated into a practical application (see MPEP 2106.04(d)I.), failing Step 2A Prong 2. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception under step 2B.
Regarding Claim 9:
Step 1 — Is the claim to a process, machine, manufacture, or composition of matter?
Yes, claim 9 is directed to a method i.e., a process.
Step 2A — Prong 1 Does the claim recite an abstract idea, law of nature, or natural phenomenon?
Yes, the claim recites an abstract idea.
“the accelerated optimization method comprising: a) a user choosing a CLF V convergence condition”
“b) initializing the accelerated optimization method according to
λ
x
0
= -αxL(1,
λ
s
0
,x0), s0 = e(x0) and setting k = 0;
c) computing Vk = V(z(k))
d) while stopping conditions are not met do;
d1) generate ζ(k);
d2) compute
h
k
0
;
d3) advance to (z(k + 1), x(k + 1)) using
h
k
0
d4) compute Vk + 1 = V(z(k + 1))
d5) while Vk + 1 has not decreased sufficiently do: d4a) backtrack (z(k + 1), x(k + 1)) along ζ(k);
recompute Vk + 1
d6) end while; and
d7) update k [Wingdings font/0xDF] k + 1; and
e) end while”
These limitations, under their broadest reasonable interpretation, cover mathematical concepts (including mathematical relationships, mathematical formulas or equations, mathematical calculations) and mental processes, concepts performed in the human mind (including an observation, evaluation, judgment, opinion). See MPEP 2106.04(a)(2). With regard to the mathematical concepts, in particular, the above initialization, computing, and updating processes all recite mathematical relationships, formulas, or equations. With regard to the mental processes, in particular, with the aid of pen and paper, a human can decide which CLF V convergence condition to choose. Furthermore, with the aid of pen and paper, a human can initialize an optimization problem (i.e., compute equations).
Step 2A — Prong 2 — Does the claim recite additional elements that integrate the judicial exception into a practical application?
No, there are no additional elements that integrate the judicial exception into a practical application. The additional elements:
“A method for modeling a device or process to generate a model based on a group of digital representations of the device or process characteristics” — This limitation is reciting only the idea of a solution or outcome i.e., the claim fails to recite details of how a solution to a problem is accomplished such that it amounts no more than mere instructions to apply. See MPEP 2106.05(f); See also Electric Power Group, LLC v. Alstom, S.A., 830 F.3d 1350, 1356, 119 USPQ2d 1739 (Fed. Cir. 2016).
“the method including the execution of an accelerated optimization method to classify the digital representations of the device or process associated with each digital representation” — This limitation is reciting only the idea of a solution or outcome i.e., the claim fails to recite details of how a solution to a problem is accomplished such that it amounts no more than mere instructions to apply. See MPEP 2106.05(f); See also Electric Power Group, LLC v. Alstom, S.A., 830 F.3d 1350, 1356, 119 USPQ2d 1739 (Fed. Cir. 2016).
Step 2B — Does the claim recite additional elements that amount to significantly more than the judicial exception?
No, there are no additional elements that amount to significantly more than the judicial exception.
Regarding Claim 15:
Step 1 — Is the claim to a process, machine, manufacture, or composition of matter?
Yes, claim 15 is directed to an apparatus i.e., a machine.
Step 2A — Prong 1 Does the claim recite an abstract idea, law of nature, or natural phenomenon?
Yes, the claim recites an abstract idea.
“the accelerated optimization method comprising: a) a user choosing a CLF V convergence condition”
“b) initializing the accelerated optimization method according to
λ
x
0
= -αxL(1,
λ
s
0
,x0), s0 = e(x0) and setting k = 0;
c) computing Vk = V(z(k))
d) while stopping conditions are not met do;
d1) generate ζ(k);
d2) compute
h
k
0
;
d3) advance to (z(k + 1), x(k + 1)) using
h
k
0
d4) compute Vk + 1 = V(z(k + 1))
d5) while Vk + 1 has not decreased sufficiently do: d4a) backtrack (z(k + 1), x(k + 1)) along ζ(k);
recompute Vk + 1
d6) end while; and
d7) update k [Wingdings font/0xDF] k + 1; and
e) end while”
These limitations, under their broadest reasonable interpretation, cover mathematical concepts (including mathematical relationships, mathematical formulas or equations, mathematical calculations) and mental processes, concepts performed in the human mind (including an observation, evaluation, judgment, opinion). See MPEP 2106.04(a)(2). With regard to the mathematical concepts, in particular, the above initialization, computing, and updating processes all recite mathematical relationships, formulas, or equations. With regard to the mental processes, in particular, with the aid of pen and paper, a human can decide which CLF V convergence condition to choose. Furthermore, with the aid of pen and paper, a human can initialize an optimization problem (i.e., compute equations).
Step 2A — Prong 2 — Does the claim recite additional elements that integrate the judicial exception into a practical application?
No, there are no additional elements that integrate the judicial exception into a practical application. The additional elements:
“An apparatus for processing digital representations of a group of objects and identifying within the group of objects a target object” — This limitation is reciting generic computer components at a high-level of generality (i.e., as a generic computer component performing a generic computer function) such that it amounts no more than mere instructions to apply the exception using a generic computer component. See MPEP 2106.05(f).
“the apparatus including the execution of an accelerated optimization method to identify the target object within the digital representations of the group of objects” — This limitation is reciting only the idea of a solution or outcome i.e., the claim fails to recite details of how a solution to a problem is accomplished such that it amounts no more than mere instructions to apply. See MPEP 2106.05(f); See also Electric Power Group, LLC v. Alstom, S.A., 830 F.3d 1350, 1356, 119 USPQ2d 1739 (Fed. Cir. 2016).
Step 2B — Does the claim recite additional elements that amount to significantly more than the judicial exception?
No, there are no additional elements that amount to significantly more than the judicial exception.
Regarding Claim 20:
Step 1 — Is the claim to a process, machine, manufacture, or composition of matter?
Yes, claim 20 is directed to a method for accelerating optimization.
Step 2A — Prong 1 Does the claim recite an abstract idea, law of nature, or natural phenomenon?
Yes, the claim recites an abstract idea.
“selecting a control Lyapunov function (CLF) and associated parameters for an optimization problem”
“generate an algorithm to solve the optimization problem according to λ_x^0 = -α_xL(1, λ_s^0,x^0),s^0 = e(x^0) where k is set to 0”
“until stopping conditions are reached: generating ζ(k) by solving the optimization problem”
“computing h_k^0 using at least one of a group consisting of
PNG
media_image5.png
121
538
media_image5.png
Greyscale
”
“advancing to (z(k + 1), x(k + 1)) using a three-step iterative map and h_k^0”
“computing V_k + 1 = V(z(k + 1)) until V_k + 1 has decreased to a target threshold, backtracking (z(k + 1), x(k + 1)) along ζ(k) and recomputing V_k + 1”
These limitations, under their broadest reasonable interpretation, cover mathematical concepts (including mathematical relationships, mathematical formulas or equations, mathematical calculations) and mental processes, concepts performed in the human mind (including an observation, evaluation, judgment, opinion). See MPEP 2106.04(a)(2). With regard to the mathematical concepts, in particular, the above initialization, computing, and updating processes all recite mathematical relationships, formulas, or equations. With regard to the mental processes, in particular, with the aid of pen and paper, a human can decide which CLF V convergence condition to choose. Furthermore, with the aid of pen and paper, a human can initialize an optimization problem (i.e., compute equations).
Step 2A — Prong 2 — Does the claim recite additional elements that integrate the judicial exception into a practical application?
No, there are no additional elements that integrate the judicial exception into a practical application. The additional elements:
“incrementing k to the next step” — This limitation amounts to no more than mere instructions to apply the exception and is the equivalent to mere instruction to implement the abstract idea on a computer. See MPEP 2106.05(f). Incrementing steps in an algorithm merely invokes computers or other machinery as a tool to perform an existing process.
Step 2B — Does the claim recite additional elements that amount to significantly more than the judicial exception?
No, there are no additional elements that amount to significantly more than the judicial exception.
Regarding claims 10–14 and 16–19, although varying in scope, the limitations of claims 10–14 and 16–19 are substantially the same as the limitations of claims 2–6, respectively. Thus, claims 10–14 and 16–19 are rejected using the same reasoning and analysis as claims 2–6 above, respectively.
Claim Rejections - 35 USC § 103
The following is a quotation of 35 U.S.C. 103 which forms the basis for all obviousness rejections set forth in this Office action:
A patent for a claimed invention may not be obtained, notwithstanding that the claimed invention is not identically disclosed as set forth in section 102, if the differences between the claimed invention and the prior art are such that the claimed invention as a whole would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention pertains. Patentability shall not be negated by the manner in which the invention was made.
The factual inquiries for establishing a background for determining obviousness under 35 U.S.C. 103 are summarized as follows:
1. Determining the scope and contents of the prior art.
2. Ascertaining the differences between the prior art and the claims at issue.
3. Resolving the level of ordinary skill in the pertinent art.
4. Considering objective evidence present in the application indicating obviousness or nonobviousness.
Claims 1–20 are rejected under 35 U.S.C. 103 as being unpatentable over Manek et al., (US 20210042457 A1), hereinafter “Manek”, in view of Vikas Sindhwani (US 20200189099 A1), hereinafter “Sindhwani”.
Regarding claim 1, Manek teaches:
A method for processing digital representations of a group of objects and identifying within the group of objects a target object, the method including the execution of an accelerated optimization method to identify the target object within the digital representations of the group of objects (Manek ¶0015, ¶0110: “Namely, the training data may provide time-sequential pairs of states, with each pair being formed by a current state and a future state of the physical system, with the former being an input and the latter being a target output of the dynamics model in the model's training” and “Using these methods, the following demonstrates learning the dynamics of physical models such as n-link pendulums, e.g., with reference to FIGS. 5A-6B, and shows a substantial improvement over generic networks. It is also shown how such dynamics models can be integrated into larger network systems to learn dynamics over complex output spaces. In particular, it is shown with reference to FIGS. 7A-7B how to combine the model with a variational auto-encoder (VAE) to learn dynamic ‘video textures’”—[(emphasis added) wherein the methods include processing pairs of image data (i.e., digital representation of a group of objects) to learn a target output of the model (i.e., identify the target object) demonstrating a substantial improvement over other models (i.e., accelerated optimization)]),
the accelerated optimization method comprising:
a) a user choosing a CLF V convergence condition (Manek ¶0022: “the machine learnable Lyapunov function (V(x.sub.t)) is represented at least in part by an input-convex neural network (ICNN, g(x)). The Lyapunov function V(x.sub.t) may also be learned and represented by a neural network. By specifically selecting an input-convex neural network g(x) which enforces the condition that g(x) is convex in its inputs x, it may be ensured that V(x.sub.t)) has only one global optimum, which is one of the properties of the Lyapunov function which is to be learned by the input-convex neural network”—[wherein the BRI of “CLF” is any Control Lyapunov Function (CLF) capable of satisfying the conditions according to the method, and wherein the BRI of CLF V convergence condition is any condition that causes the Control Lyapunov Function (CLF) to decrease, driving the system toward stability, and wherein the condition is specifically selected (i.e., chosen by a user) to ensure that the model has only one global optimum (e.g., global asymptotic stability, i.e., convergence)]);
Manek does not appear to explicitly teach:
b) initializing the accelerated optimization method according to
λ
x
0
= -αxL(1,
λ
s
0
,x0),s0 = e(x0) and setting k = 0;
c) computing Vk = V(z(k));
d) while stopping conditions are not met do;
d1) generate ζ(k);
d2) compute
h
k
0
;
d3) advance to (z(k + 1), x(k + 1)) using
h
k
0
d4) compute Vk + 1 = V(z(k + 1))
d5) while Vk + 1 has not decreased sufficiently do: d4a) backtrack (z(k + 1), x(k + 1)) along ζ(k);
recompute Vk + 1
d6) end while; and
d7) update k [Wingdings font/0xDF] k + 1; and
e) end while.
However, Sindhwani teaches:
b) initializing the accelerated optimization method according to
λ
x
0
= -αxL(1,
λ
s
0
,x0), s0 = e(x0) and setting k = 0 (Sindhwani Eqs. 1, 2, ¶¶0034–0036: “Starting from an initial condition … given desired equilibria, Z={(x*i, x*1), t = 0 … Ti, i=1 … N} … In some implementations, the constraints of Equation 2 ensure incremental stability. Additionally, the constraints of Equation 2 help induce a contraction tube around an intended trajectory, such that the dynamical system evolution from a large set of initial conditions returns to the intended trajectory”—[wherein the BRI of the equation
λ
x
0
is any Control Lyapunov Function capable of satisfying the conditions according to the method, and wherein Sindhwani teaches that the constraints of Equations 1 & 2 satisfy the conditions (e.g., incremental stability, i.e., convergence to a target) according to the set of initial conditions (i.e., initializing the accelerated optimization method). Examiner notes that Sindhwani’s Equations 1 and 2 are functional equivalents of the instant application’s equations. That is, Sindhwani’s equations may be substituted for the variable placeholder equations of the instant application (e.g.,
λ
x
0
= -αxL(1,
λ
s
0
,x0), s0 = e(x0)) to accomplish the overall goal of target stability utilizing the CLF]);
c) computing Vk = V(z(k)) (Sindhwani Eq. 3, ¶¶0042–0043: “Lyapunov's direct method is a classical framework for verifying stability properties of nonlinear dynamical systems. If a suitable positive-definite scalar function can be found that decreases along the trajectories of the system, then the evolution of the system can be thought of as continuously dissipating a generalized notion of energy, eventually reaching an equilibrium point as a consequence. A ball rolling down a mountainous landscape to the deepest point in a valley is a useful mental image of a system evolving along an energy landscape induced by a Lyapunov function. In some of these implementations, energy dissipation is stated as follows: if a dynamical system {dot over (x)}=ƒ(x) can be associated with a function V(x) that has a local or global minimum at x* and whose time derivative is negative everywhere or in the vicinity of x*, i.e.,
PNG
media_image6.png
55
302
media_image6.png
Greyscale
the system is certified to be at least one of locally or globally stable”—[wherein the suitable positive-definite scalar function (i.e.,
h
k
0
) is found by continuously computing V(x) for the global minimum at x (i.e., computing Vk)]);
d) while stopping conditions are not met do, d1) generate ζ(k), d2) compute
h
k
0
, d3) advance to (z(k + 1), x(k + 1)) using
h
k
0
, d4) compute Vk + 1 = V(z(k + 1)) (Sindhwani ¶¶0044–0045: “stable linear systems admit a quadratic Lyapunov function that can be found via semi-definite programming. If a polynomial dynamical system admits a polynomial Lyapunov function, then one can search for it using sum-of-squares techniques which also reduce to instances of semi-definite programming. Value functions found by approximate dynamic programming can be used as candidate Lyapunov functions since by definition they encode “cost-to-go” which decreases along the system dynamics. Particularly relevant to this disclosure are problems like Imitation Learning and Inverse Optimal Control where cost functionals are unknown, or in settings where closed-loop dynamics of policies without corresponding value functions needs to be studied. Another aspect of the present disclosure is a technique for performing the optimization problem, set forth in Equation 1 and Equation 2, to ensure stability in the dynamical system using incremental stability and contraction analysis”—[wherein the BRI of stopping conditions is any condition that leads to system stability (i.e., the target), and wherein generating ζ(k) includes computing Vk in the previous step, and wherein approximate dynamic programming (i.e., computing) is used to find candidate Lyapunov functions (i.e., generate). Examiner notes that Lyapunov functions are found by setting the target to 0 (i.e., k=0; e.g., global minimum) and then implementing methods to acquire the functions that lead the system to the target (e.g., present disclosure paragraphs [0163, 0168])]);
d5) while Vk + 1 has not decreased sufficiently do: d4a) backtrack (z(k + 1), x(k + 1)) along ζ(k) (Sindhwani ¶¶0044–0046: “Value functions found by approximate dynamic programming can be used as candidate Lyapunov functions since by definition they encode “cost-to-go” which decreases along the system dynamics. Particularly relevant to this disclosure are problems like Imitation Learning and Inverse Optimal Control where cost functionals are unknown, or in settings where closed-loop dynamics of policies without corresponding value functions needs to be studied … In some implementations, an approach using incremental stability and contraction analysis may be utilized”—[wherein the BRI of backtracking is recomputing Vk+1 and incrementing k to the next step (i.e., updating k) see present disclosure paragraph [0041]. Examiner notes that “backtracking” is a key tenant of Control Lyapunov Functions and is effectively just implementing the “do-while” loop. Wherein the value functions are found by performing the approximate dynamic programming (i.e., do-while) which decreases incrementally during analysis (i.e., do-while the functions have not sufficiently decreased) along the system dynamics until the control function is learned]);
recompute Vk + 1, d6) end while, and d7) update k [Wingdings font/0xDF] k + 1; and e) end while (Sindhwani ¶¶0046, 0049–0050, 0054, 0124: “an approach using incremental stability and contraction analysis may be utilized. Incremental stability is concerned with the convergence of system trajectories with respect to each other, as opposed to stability with respect to a single equilibrium, as utilized in the Lyapunov analysis. Contraction analysis derives sufficient conditions under which the displacement between any two trajectories x(t,x.sub.0) and x(t,x.sub.1) starting from the initial conditions x.sub.0 and x.sub.1 will go to zero, or the target position. In some of these implementations, if ƒ is continuously differentiable, then {dot over (x)}=ƒ(x) implies the differential relation” and “the search for a contraction metric may be interpreted as the search for a Lyapunov function of the specific form V(x)=ƒ(x).sup.TM(x)ƒ(x)” and “CLF-DM is another dynamical system approach for learning nonlinear dynamical systems. In some implementations, CLF-DM may learn a parametric Lyapunov function from a set of given demonstration trajectories. Various regression techniques may be utilized to learn an unstable dynamical system from the set of given demonstration trajectories. The learned control Lyapunov function may be utilized to derive a command to stabilize the learned unstable dynamical system from the set of given demonstration trajectories” and “The training for the control policy system was conducted for 6000 iterations”—[(emphasis added) wherein the system learns (i.e., do-while) until the control Lyapunov function is learned (i.e., end-while), and wherein the system iterates (i.e., do-while) using incremental stability and contraction analysis (i.e., k [Wingdings font/0xDF] k+1) updating k with k+1 (e.g., incremental steps)]).
The methods of Manek, the teachings of Sindhwani, and the instant application are analogous art because they pertain to utilizing machine learning models with Control Lyapunov Functions to reach a target.
It would be obvious to a person of ordinary skill in the art before the effective filing date of the invention to modify the methods of Manek with the teachings of Sindhwani to provide specific algorithmic equivalencies to the instant application for utilizing optimization methods to reach a target. One would be motivated to do so to improve generation of functions that lead to dynamic system stability i.e., a target (Sindhwani ¶0033: “Implementations of this specification are related to various improvements in generating a control policy that regulates both motion control and robot interaction with the environment and/or that includes a learned non-parametric potential function and/or dissipative field. In some implementations, the improvements improve performance of the control policy, improve learning of the potential function and/or dissipative field of the control policy, and/or achieve other benefits”).
Regarding claim 2, Manek in view of Sindhwani teaches all the limitations of claim 1.
Manek teaches:
wherein step a) of the accelerated optimization method includes: a user choosing a CLF V convergence condition and the parameters associated with a Problem (P) or (P*) (Manek ¶0022: “Optionally, the machine learnable Lyapunov function (V(x.sub.t)) is represented at least in part by an input-convex neural network (ICNN, g(x)). The Lyapunov function V(x.sub.t) may also be learned and represented by a neural network. By specifically selecting an input-convex neural network g(x) which enforces the condition that g(x) is convex in its inputs x, it may be ensured that V(x.sub.t)) has only one global optimum, which is one of the properties of the Lyapunov function which is to be learned by the input-convex neural network”—[wherein the user chooses by specifically selecting an input-convex neural network g(x) which enforces the condition that g(x) is convex in its inputs x (i.e., choosing a convergence condition and the parameters)]); and
wherein step d1) includes generating ζ(k) by solving Problem (P*)( or (P)) (Manek ¶0112: “Lyapunov analysis says that ƒ is stable (according to the definitions above) if and only if we can find some function V as above such the value of this function is decreasing along trajectories generated by ƒ. Formally, this is the condition that the time derivative {dot over (V)}(x(t))<0”—[wherein the analysis is performed to find the function V (i.e., generating ζ(k) by solving the problem)]).
Regarding claim 3, Manek in view of Sindhwani teaches all the limitations of claim 1.
Sindhwani teaches:
wherein step d2) includes: computing h_k^0 using, M_1(k) [h_k^BL^X] + h_k^BLM_2(k)X = b_k, where M_1(k), M_2(k) and b_k are matrices (of appropriate dimensions) that depend on the known values of iterates of at point k, and X is a variable that comprises za(k + 1), ψ_ λ_x, ψ_ λ_y, ψ_ λ_s, ψ_ v, ψ_s and ψ_ x, the known values of iterates given by:
PNG
media_image2.png
204
494
media_image2.png
Greyscale
(Sindhwani Eqs. 4, 5, Definition 1, ¶¶0005, 0015, 0046–0049, 0058–0059: “K(x, y) returns an n×n matrix … the ln×ln Gram matric of K defined by the n×n blocks”).
The same motivation that was utilized for combining Manek with Sindhwani, as set forth in claim 1, is equally applicable to claim 3.
Regarding claim 4, Manek in view of Sindhwani teaches all the limitations of claim 1.
Sindhwani teaches:
wherein step d2) includes: computing h_k^0 using,
PNG
media_image3.png
389
545
media_image3.png
Greyscale
(Sindhwani Eqs. 6–12, ¶¶0061–0072: “In some of these implementations, the matrix-valued feature map for Gaussian separable kernels and curl-free kernels may define the random scalar feature map”—[wherein step d2 includes finding the step size for the equation (see present disclosure [0161]) based on a map]).
The same motivation that was utilized for combining Manek with Sindhwani, as set forth in claim 1, is equally applicable to claim 4.
Regarding claim 5, Manek in view of Sindhwani teaches all the limitations of claim 1.
Sindhwani teaches:
wherein step d2) includes: computing hk using
PNG
media_image7.png
59
201
media_image7.png
Greyscale
(Sindhwani Eqs. 9, 10, ¶¶0053, 0065–0067: “In some implementations, SEDS may utilize a Gaussian mixture model to represent the dynamical system control policy, and may impose constraints on means and covariance of Gaussian mixtures to ensure global asymptotic stability of the trained model. The stability in SEDS is based on a simple quadratic Lyapunov function as disclosed herein” and “In some implementations, curl-free kernels may be defined by the Hessian of the scalar Gaussian kernel … where vector fields in the associated RKHS are curl-free and can be interpreted as gradient flows with respect to a potential field V … Consequently, the Jacobian of ƒ, J.sub.ƒ=−∇.sup.2V, at any x is symmetric being the Hessian of −V”).
The same motivation that was utilized for combining Manek with Sindhwani, as set forth in claim 1, is equally applicable to claim 5.
Regarding claim 6, Manek in view of Sindhwani teaches all the limitations of claim 1.
Sindhwani teaches:
wherein step d3) includes: advancing to (z(k + 1), x(k + 1)) using h_k^0 and
PNG
media_image1.png
185
454
media_image1.png
Greyscale
(Sindhwani Eqs. 13–15, ¶¶0073–0076: “much like generating a subspace of RKHS vector fields from K to K.sup.Z, it may be desirable to generate a subspace of a matrix-value feature map from Φ to Φ.sup.Z, such that Φ.sup.Z(x) vanishes on Z … n some implementations, a regression with LMI constraints may be performed. For example, by using matrix-valued random feature approximation to kernels, the learned vector field may have the form … In some implementations, a regression with LMI constraints may be performed on the reduced optimization problem, set forth in Equation 17 and Equation 18. The regression solves the problems set forth herein while ensuring optimal performance at inference time. Note that the contraction constraints in Equation 18 may be enforced only for a subsample of points. Slack variables may be added to ensure feasibility”—[wherein the BRI of advancing (similar to backtracking) incrementing k to the next step (i.e., computing k + 1) see present disclosure paragraph [0041], and wherein Sindhwani’s method performs the regression by advancing through the map from k to kz and Φ to Φz (i.e., advancing)]).
The same motivation that was utilized for combining Manek with Sindhwani, as set forth in claim 1, is equally applicable to claim 6.
Regarding claim 7, Manek in view of Sindhwani teaches all the limitations of claim 1.
Manek teaches:
wherein the digital representations of a group of objects includes a plurality of object pixel images and the target object is a pixel image of the target image (Manek ¶0129: “The overall network may be trained on pairs of successive frames sampled from videos. To generate video textures, the dynamics model may be seeded with the encoding of a single frame and the dynamics model may be numerically integrated to obtain a trajectory. The VAE decoder may convert each step of the trajectory into a frame”—[wherein sampled video frames (i.e., plurality of object pixel images) are used to seed the encoding of a single frame (i.e., the target object is a pixel image of the target image)]).
Regarding claim 8, Manek in view of Sindhwani teaches all the limitations of claim 1.
Manek teaches:
wherein the digital representations of a group of objects includes a plurality of objects associated with characteristics of a device or process and the target object is a target object associated with a target characteristic of the device or process (Manek ¶¶0129–0130: “FIG. 7B shows trajectories projected onto a two-dimensional plane for, from left to right, three different runs of the dynamics model with the stability constraint and for a dynamics model without the stability constraint in the form of a generic neural network. In this example, the true latent space is 320-dimensional, and the trajectories may be projected onto a two-dimensional plane for display. For the non-stable model, the dynamics quickly diverge and produce a static image, whereas for the stable model, it is possible to generate different (stable) trajectories that keep generating realistic images over long time horizons”—[wherein sampled video frames are associated with generating video textures (i.e., characteristics of a device or process) and wherein the realistic images are the target object of the device or process from the generated stable trajectories]).
Regarding claim 20, Manek teaches:
selecting a control Lyapunov function (CLF) and associated parameters for an optimization problem (Manek ¶0103, 0022: “wherein said learning is constrained to provide a globally stable modelling of the dynamics of the physical system by jointly learning the dynamics model and the Lyapunov function so that values of the learned Lyapunov function decrease along all trajectories of states inferred by the learned dynamics model” and “the machine learnable Lyapunov function (V(x.sub.t)) is represented at least in part by an input-convex neural network (ICNN, g(x)). The Lyapunov function V(x.sub.t) may also be learned and represented by a neural network. By specifically selecting an input-convex neural network g(x) which enforces the condition that g(x) is convex in its inputs x, it may be ensured that V(x.sub.t)) has only one global optimum, which is one of the properties of the Lyapunov function which is to be learned by the input-convex neural network”—[wherein the BRI of “CLF” is any Control Lyapunov Function (CLF) capable of satisfying the conditions according to the method, and wherein the condition (i.e., CLF and parameters) is specifically selected (i.e., chosen by a user) to ensure that the model has only one global optimum (e.g., global asymptotic stability, i.e., convergence)]);
Manek does not appear to explicitly teach:
generate an algorithm to solve the optimization problem according to
λ
x
0
= -αxL(1,
λ
s
0
,x0),s0 = e(x0), where k is set to 0;
until stopping conditions are reached:
generating ζ(k) by solving the optimization problem;
computing
h
k
0
using at least one of a group consisting of
PNG
media_image8.png
126
550
media_image8.png
Greyscale
advancing to (z(k + 1), x(k + 1)) using a three-step iterative map and
h
k
0
;
computing Vk+1 = V(z(k +1));
until Vk+1 has decreased to a target threshold, backtracking (z(k + 1), x(k+ 1)) along ζ(k) and recomputing Vk+1; and
incrementing k to the next step.
However, Sindhwani teaches:
generate an algorithm to solve the optimization problem according to
λ
x
0
= -αxL(1,
λ
s
0
,x0),s0 = e(x0), where k is set to 0 (Sindhwani Eqs. 1, 2, ¶¶0034–0036: “Starting from an initial condition … given desired equilibria, Z={(x*i, x*1), t = 0 … Ti, i=1 … N} … In some implementations, the constraints of Equation 2 ensure incremental stability. Additionally, the constraints of Equation 2 help induce a contraction tube around an intended trajectory, such that the dynamical system evolution from a large set of initial conditions returns to the intended trajectory”—[wherein the BRI of the equation
λ
x
0
is any Control Lyapunov Function capable of satisfying the conditions according to the method, and wherein Sindhwani teaches that the constraints of Equations 1 & 2 satisfy the conditions (e.g., incremental stability, i.e., convergence to a target) according to the set of initial conditions (i.e., initializing the accelerated optimization method). Examiner notes that Sindhwani’s Equations 1 and 2 are functional equivalents of the instant application’s equations. That is, Sindhwani’s equations may be substituted for the variable placeholder equations of the instant application (e.g.,
λ
x
0
= -αxL(1,
λ
s
0
,x0), s0 = e(x0)) to accomplish the overall goal of target stability utilizing the CLF]);
until stopping conditions are reached (Sindhwani ¶¶0044–0045: “stable linear systems admit a quadratic Lyapunov function that can be found via semi-definite programming. If a polynomial dynamical system admits a polynomial Lyapunov function, then one can search for it using sum-of-squares techniques which also reduce to instances of semi-definite programming. Value functions found by approximate dynamic programming can be used as candidate Lyapunov functions since by definition they encode “cost-to-go” which decreases along the system dynamics. Particularly relevant to this disclosure are problems like Imitation Learning and Inverse Optimal Control where cost functionals are unknown, or in settings where closed-loop dynamics of policies without corresponding value functions needs to be studied. Another aspect of the present disclosure is a technique for performing the optimization problem, set forth in Equation 1 and Equation 2, to ensure stability in the dynamical system using incremental stability and contraction analysis”—[wherein the BRI of stopping conditions is any condition that leads to system stability (i.e., the target), causes the Control Lyapunov Function (CLF) to decrease, driving the system toward stability. Examiner notes that Lyapunov functions are found by setting the target to 0 (i.e., k=0; e.g., global minimum) and then implementing methods to acquire the functions that lead the system to the target (e.g., present disclosure paragraphs [0163, 0168])):
generating ζ(k) by solving the optimization problem (Sindhwani ¶¶0042–0045: “Lyapunov's direct method is a classical framework for verifying stability properties of nonlinear dynamical systems. If a suitable positive-definite scalar function can be found that decreases along the trajectories of the system, then the evolution of the system can be thought of as continuously dissipating a generalized notion of energy, eventually reaching an equilibrium point as a consequence. A ball rolling down a mountainous landscape to the deepest point in a valley is a useful mental image of a system evolving along an energy landscape induced by a Lyapunov function … stable linear systems admit a quadratic Lyapunov function that can be found via semi-definite programming. If a polynomial dynamical system admits a polynomial Lyapunov function, then one can search for it using sum-of-squares techniques which also reduce to instances of semi-definite programming. Value functions found by approximate dynamic programming can be used as candidate Lyapunov functions since by definition they encode “cost-to-go” which decreases along the system dynamics. Particularly relevant to this disclosure are problems like Imitation Learning and Inverse Optimal Control where cost functionals are unknown, or in settings where closed-loop dynamics of policies without corresponding value functions needs to be studied. Another aspect of the present disclosure is a technique for performing the optimization problem, set forth in Equation 1 and Equation 2, to ensure stability in the dynamical system using incremental stability and contraction analysis”—[wherein generating ζ(k) includes computing Vk, and wherein approximate dynamic programming (i.e., computing) is used to find candidate Lyapunov functions (i.e., generate). Examiner notes that Lyapunov functions are found by setting the target to 0 (i.e., k=0; e.g., global minimum) and then implementing methods to acquire the functions that lead the system to the target (e.g., present disclosure paragraphs [0163, 0168])]);
computing
h
k
0
using at least one of a group consisting of
PNG
media_image8.png
126
550
media_image8.png
Greyscale
(Sindhwani Eqs. 1–12, Definition 1, ¶¶0005, 0015, 0044–0049, 0053, 0058–0059, 0061–0072: “K(x, y) returns an n×n matrix … the ln×ln Gram matric of K defined by the n×n blocks” and “stable linear systems admit a quadratic Lyapunov function that can be found via semi-definite programming. If a polynomial dynamical system admits a polynomial Lyapunov function, then one can search for it using sum-of-squares techniques which also reduce to instances of semi-definite programming. Value functions found by approximate dynamic programming can be used as candidate Lyapunov functions since by definition they encode “cost-to-go” which decreases along the system dynamics. Particularly relevant to this disclosure are problems like Imitation Learning and Inverse Optimal Control where cost functionals are unknown, or in settings where closed-loop dynamics of policies without corresponding value functions needs to be studied. Another aspect of the present disclosure is a technique for performing the optimization problem, set forth in Equation 1 and Equation 2, to ensure stability in the dynamical system using incremental stability and contraction analysis” and “In some of these implementations, the matrix-valued feature map for Gaussian separable kernels and curl-free kernels may define the random scalar feature map” and “In some implementations, SEDS may utilize a Gaussian mixture model to represent the dynamical system control policy, and may impose constraints on means and covariance of Gaussian mixtures to ensure global asymptotic stability of the trained model. The stability in SEDS is based on a simple quadratic Lyapunov function as disclosed herein” and “In some implementations, curl-free kernels may be defined by the Hessian of the scalar Gaussian kernel … where vector fields in the associated RKHS are curl-free and can be interpreted as gradient flows with respect to a potential field V … Consequently, the Jacobian of ƒ, J.sub.ƒ=−∇.sup.2V, at any x is symmetric being the Hessian of −V” ”—[wherein step d2 includes finding the step size for the equation (see present disclosure [0161]) based on a map]);
advancing to (z(k + 1), x(k + 1)) using a three-step iterative map and
h
k
0
(Sindhwani Eqs. 1–12, ¶¶0034, 0044–0045, 0061–0072: “The following optimization may be performed over a non-parametric family, Figure HZ, of vector-valued maps vanishing on the desired equilibria, Z” and “stable linear systems admit a quadratic Lyapunov function that can be found via semi-definite programming. If a polynomial dynamical system admits a polynomial Lyapunov function, then one can search for it using sum-of-squares techniques which also reduce to instances of semi-definite programming. Value functions found by approximate dynamic programming can be used as candidate Lyapunov functions since by definition they encode “cost-to-go” which decreases along the system dynamics. Particularly relevant to this disclosure are problems like Imitation Learning and Inverse Optimal Control where cost functionals are unknown, or in settings where closed-loop dynamics of policies without corresponding value functions needs to be studied. Another aspect of the present disclosure is a technique for performing the optimization problem, set forth in Equation 1 and Equation 2, to ensure stability in the dynamical system using incremental stability and contraction analysis” and “In some of these implementations, the matrix-valued feature map for Gaussian separable kernels and curl-free kernels may define the random scalar feature map”—[(emphasis added) wherein the CLF process is an incremental process (i.e., iterative) based on a multi-step map]);
computing Vk+1 = V(z(k +1)) (Sindhwani Eqs. 1–4, ¶¶0042–0045: “Lyapunov's direct method is a classical framework for verifying stability properties of nonlinear dynamical systems. If a suitable positive-definite scalar function can be found that decreases along the trajectories of the system, then the evolution of the system can be thought of as continuously dissipating a generalized notion of energy, eventually reaching an equilibrium point as a consequence. A ball rolling down a mountainous landscape to the deepest point in a valley is a useful mental image of a system evolving along an energy landscape induced by a Lyapunov function. In some of these implementations, energy dissipation is stated as follows: if a dynamical system {dot over (x)}=ƒ(x) can be associated with a function V(x) that has a local or global minimum at x* and whose time derivative is negative everywhere or in the vicinity of x*, i.e.,
PNG
media_image6.png
55
302
media_image6.png
Greyscale
the system is certified to be at least one of locally or globally stable … stable linear systems admit a quadratic Lyapunov function that can be found via semi-definite programming. If a polynomial dynamical system admits a polynomial Lyapunov function, then one can search for it using sum-of-squares techniques which also reduce to instances of semi-definite programming. Value functions found by approximate dynamic programming can be used as candidate Lyapunov functions since by definition they encode “cost-to-go” which decreases along the system dynamics. Particularly relevant to this disclosure are problems like Imitation Learning and Inverse Optimal Control where cost functionals are unknown, or in settings where closed-loop dynamics of policies without corresponding value functions needs to be studied. Another aspect of the present disclosure is a technique for performing the optimization problem, set forth in Equation 1 and Equation 2, to ensure stability in the dynamical system using incremental stability and contraction analysis”—[wherein the suitable positive-definite scalar function (i.e.,
h
k
0
) is found by continuously computing V(x) for the global minimum at x (i.e., computing Vk + 1)];
until Vk+1 has decreased to a target threshold, backtracking (z(k + 1), x(k+ 1)) along ζ(k) and recomputing Vk+1 (Sindhwani ¶¶0044–0046, 0080: “Value functions found by approximate dynamic programming can be used as candidate Lyapunov functions since by definition they encode “cost-to-go” which decreases along the system dynamics. Particularly relevant to this disclosure are problems like Imitation Learning and Inverse Optimal Control where cost functionals are unknown, or in settings where closed-loop dynamics of policies without corresponding value functions needs to be studied … In some implementations, an approach using incremental stability and contraction analysis may be utilized” and “In some cases the non-parametric potential function may have a global minimum that is based on target point(s) of the group(s) of data points. In some of those implementations, the learning engine 124 further utilizes the group(s) of data points in learning a dissipative field for use in the control policy. In some implementations, the learning engine 124 solves constrained optimization problem(s) in learning the potential function and/or the dissipative field. While the global minimum of a learned potential function will be based on target point(s) of the groups(s) of data points, it is understood that in many situations it will not strictly conform to the target point(s). Moreover, where multiple target point(s) of multiple group(s) are provided, it is understood that those target point(s) may not all strictly conform to one another”—[wherein the BRI of backtracking is recomputing Vk+1 and incrementing k to the next step (i.e., updating k) see present disclosure paragraph [0041]. Examiner notes that “backtracking” is a key tenant of Control Lyapunov Functions and is effectively just implementing the “do-while” loop. Wherein the value functions are found by performing the approximate dynamic programming (i.e., do-while) which decreases incrementally during analysis (i.e., do-while the functions have not decreased to the target point (i.e., threshold)) along the system dynamics until the control function is learned]); and
incrementing k to the next step (Sindhwani ¶¶0046, 0049–0050, 0054, 0094, 0124: “an approach using incremental stability and contraction analysis may be utilized. Incremental stability is concerned with the convergence of system trajectories with respect to each other, as opposed to stability with respect to a single equilibrium, as utilized in the Lyapunov analysis. Contraction analysis derives sufficient conditions under which the displacement between any two trajectories x(t,x.sub.0) and x(t,x.sub.1) starting from the initial conditions x.sub.0 and x.sub.1 will go to zero, or the target position. In some of these implementations, if ƒ is continuously differentiable, then {dot over (x)}=ƒ(x) implies the differential relation” and “the search for a contraction metric may be interpreted as the search for a Lyapunov function of the specific form V(x)=ƒ(x).sup.TM(x)ƒ(x)” and “CLF-DM is another dynamical system approach for learning nonlinear dynamical systems. In some implementations, CLF-DM may learn a parametric Lyapunov function from a set of given demonstration trajectories. Various regression techniques may be utilized to learn an unstable dynamical system from the set of given demonstration trajectories. The learned control Lyapunov function may be utilized to derive a command to stabilize the learned unstable dynamical system from the set of given demonstration trajectories” and “The training for the control policy system was conducted for 6000 iterations” and “By using this method, the control policy system is incrementally stabilized because it sets up a region of stability around the demonstration trajectories for a given shape, pattern, or combination thereof. This incremental stability allows the control policy system to better generalize, from any starting point, a control policy and “pull” perturbations toward the intended trajectory in a dynamic environment should the robot encounter an obstacle, e.g., a moving or transient object in the dynamic environment”—[(emphasis added) wherein the system learns (i.e., do-while) until the control Lyapunov function is learned (i.e., end-while), and wherein the system iterates (i.e., do-while) using incremental stability and contraction analysis (i.e., k [Wingdings font/0xDF] k+1) updating k with k+1 (e.g., incremental steps)]).
The methods of Manek, the teachings of Sindhwani, and the instant application are analogous art because they pertain to utilizing machine learning models with Control Lyapunov Functions to reach a target.
It would be obvious to a person of ordinary skill in the art before the effective filing date of the invention to modify the methods of Manek with the teachings of Sindhwani to provide specific algorithmic equivalencies to the instant application for utilizing optimization methods to reach a target. One would be motivated to do so to improve generation of functions that lead to dynamic system stability i.e., a target (Sindhwani ¶0033: “Implementations of this specification are related to various improvements in generating a control policy that regulates both motion control and robot interaction with the environment and/or that includes a learned non-parametric potential function and/or dissipative field. In some implementations, the improvements improve performance of the control policy, improve learning of the potential function and/or dissipative field of the control policy, and/or achieve other benefits”).
Regarding claims 9 and 15, although varying in scope, the limitations of claims 9 and 15 are substantially the same as the limitations of claim 1. Thus, claims 9 and 15 are rejected using the same reasoning and analysis as claim 1 above.
Regarding claims 10–14 and 16–19, although varying in scope, the limitations of claims 10–14 and 16–19 are substantially the same as the limitations of claims 2–6, respectively. Thus, claims 10–14 and 16–19 are rejected using the same reasoning and analysis as claims 2–6 above, respectively.
Prior Art of Record
The prior art made of record and not relied upon is considered pertinent to applicant’s disclosure.
Zhang et al., (“Augmented two-side-looped Lyapunov functional for sampled-data-based synchronization of chaotic neural networks with actuator saturation”) discloses methods for investigating image processing problems using Lyapunov functions “This paper further investigated the synchronization problem of the chaotic neural networks by utilizing the sampled-data control with actuator saturation. Firstly, an augmented two-side-looped Lyapunov functional including both the states of the error system and their derivative is constructed. Then the Wirtinger-based integral inequality in combination with the improved reciprocally convex matrix inequality is applied to estimate the derivative of the presented Lyapunov functional and improved synchronization criteria are derived. As a result, a state feedback controller based on sampled-data is designed, making the drive system synchronize with the response system. Finally, through the results of the numerical example, the validity and superiority of the proposed methods have been confirmed.” Zhang Abstract.
Anastasia Borovykh, (“A Gaussian Process perspective on Convolutional Neural Networks”) discloses methods for using Gaussian processes including Control Lyapunov functions for convolution neural network problems “In this paper we cast the well-known convolutional neural network in a Gaussian process perspective. In this way we hope to gain additional insights into the performance of convolutional networks, in particular understand under what circumstances they tend to perform well and what assumptions are implicitly made in the network. While for fully-connected networks the properties of convergence to Gaussian processes have been studied extensively, little is known about situations in which the output from a convolutional network approaches a multivariate normal distribution.” Borovykh Abstract.
Conclusion
Any inquiry concerning this communication or earlier communications from the examiner should be directed to NICHOLAS SHINE whose telephone number is (571)272-2512. The examiner can normally be reached M-F, 11a-7p ET.
Examiner interviews are available via telephone, in-person, and video conferencing using a USPTO supplied web-based collaboration tool. To schedule an interview, applicant is encouraged to use the USPTO Automated Interview Request (AIR) at http://www.uspto.gov/interviewpractice.
If attempts to reach the examiner by telephone are unsuccessful, the examiner’s supervisor, David Yi can be reached on (571) 270-7519. The fax phone number for the organization where this application or proceeding is assigned is 571-273-8300.
Information regarding the status of published or unpublished applications may be obtained from Patent Center. Unpublished application information in Patent Center is available to registered users. To file and manage patent submissions in Patent Center, visit: https://patentcenter.uspto.gov. Visit https://www.uspto.gov/patents/apply/patent-center for more information about Patent Center and https://www.uspto.gov/patents/docx for information about filing in DOCX format. For additional questions, contact the Electronic Business Center (EBC) at 866-217-9197 (toll-free). If you would like assistance from a USPTO Customer Service Representative, call 800-786-9199 (IN USA OR CANADA) or 571-272-1000.
/N.B.S./Examiner, Art Unit 2126
/DAVID YI/Supervisory Patent Examiner, Art Unit 2126
Prosecution Insights