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Concurrent learning-based approximate optimal regulation

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Rushikesh Kamalapurkar, Patrick Walters, Warren Dixon

Systems and Control · Submitted 11 Apr 2013

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim This paper presents a concurrent learning-based solution to the online approximate optimal regulation problem that eliminates the need for PE.

how it is stated · asserted 1.00 read the record →

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arXiv ID1304.3477 (version 1)
Pith IDFMVDBHLP, Pith's permanent record of this paper and its review
CitationPatrick Walters, Rushikesh Kamalapurkar, Warren Dixon. "Concurrent learning-based approximate optimal regulation." arXiv:1304.3477 (2013). https://pith.science/paper/FMVDBHLP
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,325 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.30 · human participants 0.02 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.72 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

In deterministic systems, reinforcement learning-based online approximate optimal control methods typically require a restrictive persistence of excitation (PE) condition for convergence. This paper presents a concurrent learning-based solution to the online approximate optimal regulation problem that eliminates the need for PE. The development is based on the observation that given a model of the system, the Bellman error, which quantifies the deviation of the system Hamiltonian from the optimal Hamiltonian, can be evaluated at any point in the state space. Further, a concurrent learning-based parameter identifier is developed to compensate for parametric uncertainty in the plant dynamics. Uniformly ultimately bounded (UUB) convergence of the system states to the origin, and UUB convergence of the developed policy to the optimal policy are established using a Lyapunov-based analysis, and simulations are performed to demonstrate the performance of the developed controller.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In deterministic systems, reinforcement learning-based online approximate optimal control methods typically require a restrictive persistence of excitation (PE) condition for convergence. background 0.95 0.05 0.03 asserted 1.00
s1 This paper presents a concurrent learning-based solution to the online approximate optimal regulation problem that eliminates the need for PE. contribution 1.00 0.94 0.83 asserted 1.00
s2 The development is based on the observation that given a model of the system, the Bellman error, which quantifies the deviation of the system Hamiltonian from the optimal Hamiltonian, can be evaluated at any point in the state space. method 0.90 0.52 0.05 asserted 0.97
s3 Further, a concurrent learning-based parameter identifier is developed to compensate for parametric uncertainty in the plant dynamics. method 0.61 0.95 0.05 asserted 1.00
s4 Uniformly ultimately bounded (UUB) convergence of the system states to the origin, and UUB convergence of the developed policy to the optimal policy are established using a Lyapunov-based analysis, and simulations are performed to demonstrate the performance of the developed controller. result 0.95 0.96 0.48 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from proof or derivation 0.95.

What was examined, and what was not

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  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

In deterministic systems, reinforcement learning-based online approximate optimal control methods typically require a restrictive persistence of excitation (PE) condition for convergence. This paper presents a concurrent learning-based solution to the online approximate optimal regulation problem that eliminates the need for PE. The development is based on the observation that given a model of the system, the Bellman error, which quantifies the deviation of the system Hamiltonian from the optimal Hamiltonian, can be evaluated at any point in the state space. Further, a concurrent learning-based parameter identifier is developed to compensate for parametric uncertainty in the plant dynamics. Uniformly ultimately bounded (UUB) convergence of the system states to the origin, and UUB convergence of the developed policy to the optimal policy are established using a Lyapunov-based analysis, and simulations are performed to demonstrate the performance of the developed controller.

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