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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Bibliographic Details
Published in:IEEE transaction on neural networks and learning systems Vol. 33; no. 1; pp. 270 - 280
Main Authors: Li, Jinna, Ding, Jinliang, Chai, Tianyou, Lewis, Frank L., Jagannathan, Sarangapani
Format: Journal Article
Language:English
Published: United States IEEE 01.01.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:2162-237X
2162-2388
2162-2388
DOI:10.1109/TNNLS.2020.3027653