Adaptive Interleaved Reinforcement Learning: Robust Stability of Affine Nonlinear Systems With Unknown Uncertainty

This article investigates adaptive robust controller design for discrete-time (DT) affine nonlinear systems using an adaptive dynamic programming. A novel adaptive interleaved reinforcement learning algorithm is developed for finding a robust controller of DT affine nonlinear systems subject to matc...

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Vydané v:	IEEE transaction on neural networks and learning systems Ročník 33; číslo 1; s. 270 - 280
Hlavní autori:	Li, Jinna, Ding, Jinliang, Chai, Tianyou, Lewis, Frank L., Jagannathan, Sarangapani
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	United States IEEE 01.01.2022 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:	Adaptive learning Adaptive systems Algorithms Control systems design Controllers Discrete time systems Dynamic programming Interleaved reinforcement learning Linear systems Machine learning Neural networks neural networks (NNs) Nonlinear systems Optimal control Performance evaluation Reinforcement Robust control Robust stability Stability System effectiveness uncertain systems Uncertainty
ISSN:	2162-237X, 2162-2388, 2162-2388
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Abstract	This article investigates adaptive robust controller design for discrete-time (DT) affine nonlinear systems using an adaptive dynamic programming. A novel adaptive interleaved reinforcement learning algorithm is developed for finding a robust controller of DT affine nonlinear systems subject to matched or unmatched uncertainties. To this end, the robust control problem is converted into the optimal control problem for nominal systems by selecting an appropriate utility function. The performance evaluation and control policy update combined with neural networks approximation are alternately implemented at each time step for solving a simplified Hamilton-Jacobi-Bellman (HJB) equation such that the uniformly ultimately bounded (UUB) stability of DT affine nonlinear systems can be guaranteed, allowing for all realization of unknown bounded uncertainties. The rigorously theoretical proofs of convergence of the proposed interleaved RL algorithm and UUB stability of uncertain systems are provided. Simulation results are given to verify the effectiveness of the proposed method.
AbstractList	This article investigates adaptive robust controller design for discrete-time (DT) affine nonlinear systems using an adaptive dynamic programming. A novel adaptive interleaved reinforcement learning algorithm is developed for finding a robust controller of DT affine nonlinear systems subject to matched or unmatched uncertainties. To this end, the robust control problem is converted into the optimal control problem for nominal systems by selecting an appropriate utility function. The performance evaluation and control policy update combined with neural networks approximation are alternately implemented at each time step for solving a simplified Hamilton-Jacobi-Bellman (HJB) equation such that the uniformly ultimately bounded (UUB) stability of DT affine nonlinear systems can be guaranteed, allowing for all realization of unknown bounded uncertainties. The rigorously theoretical proofs of convergence of the proposed interleaved RL algorithm and UUB stability of uncertain systems are provided. Simulation results are given to verify the effectiveness of the proposed method. This article investigates adaptive robust controller design for discrete-time (DT) affine nonlinear systems using an adaptive dynamic programming. A novel adaptive interleaved reinforcement learning algorithm is developed for finding a robust controller of DT affine nonlinear systems subject to matched or unmatched uncertainties. To this end, the robust control problem is converted into the optimal control problem for nominal systems by selecting an appropriate utility function. The performance evaluation and control policy update combined with neural networks approximation are alternately implemented at each time step for solving a simplified Hamilton-Jacobi-Bellman (HJB) equation such that the uniformly ultimately bounded (UUB) stability of DT affine nonlinear systems can be guaranteed, allowing for all realization of unknown bounded uncertainties. The rigorously theoretical proofs of convergence of the proposed interleaved RL algorithm and UUB stability of uncertain systems are provided. Simulation results are given to verify the effectiveness of the proposed method.This article investigates adaptive robust controller design for discrete-time (DT) affine nonlinear systems using an adaptive dynamic programming. A novel adaptive interleaved reinforcement learning algorithm is developed for finding a robust controller of DT affine nonlinear systems subject to matched or unmatched uncertainties. To this end, the robust control problem is converted into the optimal control problem for nominal systems by selecting an appropriate utility function. The performance evaluation and control policy update combined with neural networks approximation are alternately implemented at each time step for solving a simplified Hamilton-Jacobi-Bellman (HJB) equation such that the uniformly ultimately bounded (UUB) stability of DT affine nonlinear systems can be guaranteed, allowing for all realization of unknown bounded uncertainties. The rigorously theoretical proofs of convergence of the proposed interleaved RL algorithm and UUB stability of uncertain systems are provided. Simulation results are given to verify the effectiveness of the proposed method.
Author	Ding, Jinliang Chai, Tianyou Li, Jinna Lewis, Frank L. Jagannathan, Sarangapani
Author_xml	– sequence: 1 givenname: Jinna orcidid: 0000-0001-9985-6308 surname: Li fullname: Li, Jinna email: lijinna_721@126.com organization: School of Information and Control Engineering, Liaoning Shihua University, Fushun, China – sequence: 2 givenname: Jinliang orcidid: 0000-0003-3735-0672 surname: Ding fullname: Ding, Jinliang email: jlding@mail.neu.edu.cn organization: State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, China – sequence: 3 givenname: Tianyou orcidid: 0000-0002-4623-1483 surname: Chai fullname: Chai, Tianyou email: tychai@mail.neu.edu.cn organization: State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, China – sequence: 4 givenname: Frank L. orcidid: 0000-0003-4074-1615 surname: Lewis fullname: Lewis, Frank L. email: lewis@uta.edu organization: UTA Research Institute, The University of Texas at Arlington, Arlington, TX, USA – sequence: 5 givenname: Sarangapani orcidid: 0000-0002-2310-3737 surname: Jagannathan fullname: Jagannathan, Sarangapani email: sarangap@mst.edu organization: Department of Electrical and Computer Engineering, Missouri University of Science and Technology, Rolla, MO, USA
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SubjectTerms	Adaptive learning Adaptive systems Algorithms Control systems design Controllers Discrete time systems Dynamic programming Interleaved reinforcement learning Linear systems Machine learning Neural networks neural networks (NNs) Nonlinear systems Optimal control Performance evaluation Reinforcement Robust control Robust stability Stability System effectiveness uncertain systems Uncertainty
Title	Adaptive Interleaved Reinforcement Learning: Robust Stability of Affine Nonlinear Systems With Unknown Uncertainty
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