rapid-communication
Authors: Jianguo Zhao, Chunyu Yang, Weinan Gao, and Ju H. Park
Volume 163, Issue C
Published: 09 July 2024 Publication History
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Abstract
The infinite-horizon zero-sum game of a linear system can be resorted to solve a Game algebraic Riccati equation (GARE) with indefinite quadratic term. Double-loop policy iteration algorithm is often used to find the solution of such GARE, but its calculation is usually time-consuming. In this work, we propose a novel model-based single-loop policy iteration algorithm to solve GARE and the convergence of the algorithm is guaranteed by the boundness of the iterative sequence and the comparison result. Furthermore, we devise a data-driven single-loop policy iteration algorithm for solving linear zero-sum games, without requiring the knowledge of system dynamics. Compared to the existing Newton’s single-loop methods, the initialization of our algorithms is significantly relaxed and easier to implement. Two numerical examples are included to illustrate the proposed algorithms.
References
[1]
Abu-Khalaf,M., Karaman,S., & Rus,D. (2019). Shared linear quadratic regulation control: A reinforcement learning approach. In IEEE 58th conference on decision and control (pp. 4569–4576). Nice, France.
[2]
Abu-Khalaf M., Lewis F.L., Huang J., Policy iterations and the Hamilton-Jacobi-Isaacs equation for H ∞ state feedback control with input saturation, IEEE Transactions on Automatic Control 51 (12) (2006) 1989–1995.
[3]
Basar T., Bernhard P., H-infinity optimal control and related minimax design problems: A dynamic game approach, Springer, New York, NY, USA, 2008.
[4]
Chen C., Lewis F.L., Li B., hom*otopic policy iteration-based learning design for unknown linear continuous-time systems, Automatica 138 (2022).
[5]
Chen C., Lewis F.L., Xie S., Modares H., Liu Z., Zuo S., et al., Resilient adaptive and H ∞ controls of multi-agent systems under sensor and actuator faults, Automatica 102 (2019) 19–26.
[6]
Fu Y., Fu J., Chai T., Robust adaptive dynamic programming of two-player zero-sum games for continuous-time linear systems, IEEE Transactions on Neural Networks and Learning Systems 26 (12) (2015) 3314–3319.
[7]
Gao W., Deng C., Jiang Y., Jiang Z.-P., Resilient reinforcement learning and robust output regulation under denial-of-service attacks, Automatica 142 (2022).
[8]
Gao W., Mynuddin M., Wunsch D.C., Jiang Z.-P., Reinforcement learning-based cooperative optimal output regulation via distributed adaptive internal model, IEEE Transactions on Neural Networks and Learning Systems 3 (10) (2022) 5229–5240.
[9]
Horn R.A., Johnson C.R., Matrix analysis, Cambridge University Press, Cambridge, U.K., 1985.
Digital Library
[10]
Ivanov I.G., Ivanov I.G., Netov N.C., On the iterative solution to H ∞ control problems, Applied Mathematics 6 (2015) 1263–1270.
[11]
Jha S.K., Roy S.B., Bhasin S., Initial excitation-based iterative algorithm for approximate optimal control of completely unknown LTI systems, IEEE Transactions on Automatic Control 64 (12) (2019) 5230–5237.
[12]
Jiang Y., Jiang Z.-P., Robust adaptive dynamic programming, Wiley-IEEE Press, Hoboken, 2017.
[13]
Jiang H., Zhou B., Bias-policy iteration based adaptive dynamic programming for unknown continuous-time linear systems, Automatica 136 (2022).
[14]
Kiumarsi B., Vamvoudakis K.G., Modares H., Lewis F.L., Optimal and autonomous control using reinforcement learning: A survey, IEEE Transactions on Neural Networks and Learning Systems 29 (6) (2018) 2042–2062.
[15]
Kleinman D., On an iterative technique for Riccati equation computations, IEEE Transactions on Automatic Control (1) (1968) 114–115.
[16]
Kolaric P., Lopez V.G., Lewis F.L., Optimal dynamic control allocation with guaranteed constraints and online reinforcement learning, Automatica 122 (2020).
[17]
Lancaster P., Rodman L., Algebraic Riccati equations, Oxford University Press, Oxford, U.K., 1995.
[18]
Lanzon A., Feng Y., Anderson B.D.O., Rotkowitz M., Computing the positive stabilizing solution to algebraic Riccati equations with an indefinite quadratic term via a recursive method, IEEE Transactions on Automatic Control 53 (10) (2008) 2280–2291.
[19]
Laub A.J., A Schur method for solving algebraic Riccati equation, IEEE Transactions on Automatic Control 24 (6) (1979) 913–921.
[20]
Li H., Liu D., Wang D., Integral reinforcement learning for linear continuous-time zero-sum games with completely unknown dynamics, IEEE Transactions on Automation Science and Engineering 11 (3) (2014) 706–714.
[21]
Li J., Xiao Z., Fan J., Chai T., Lewis F.L., Off-policy Q-learning: Solving Nash equilibrium of multi-player games with network-induced delay and unmeasured state, Automatica 136 (2022).
[22]
Lian B., Lewis F.L., Hewer G., Estabridis K., Chai T., Online learning of minmax solutions for distributed estimation and tracking control of sensor networks in graphical games, IEEE Transactions on Control of Network Systems 9 (4) (2022) 1923–1936.
[23]
Lian B., Xue W., Lewis F.L., Chai T., Inverse reinforcement learning for multi-player noncooperative apprentice games, Automatica 145 (2022).
[24]
Lin F., Robust control design: An optimal control approach, Wiley, Hoboken, NJ, USA, 2007.
[25]
Liu M., Wan Y., Lewis F.L., Lopez V.G., Adaptive optimal control for stochastic multiplayer differential games using on-policy and off-policy reinforcement learning, IEEE Transactions on Neural Networks and Learning Systems 31 (12) (2020) 5522–5533.
[26]
Liu M., Wan Y., Lopez V.G., Lewis F.L., Hewer G.A., Estabridis K., Differential graphical game with distributed global Nash solution, IEEE Transactions on Control of Network Systems 8 (3) (2021) 1371–1382.
[27]
Liu Z., Wu H.-N., New insight into the simultaneous policy update algorithms related to H ∞ state feedback control, Information Sciences 484 (2019) 84–94.
[28]
Liu D., Xue S., Zhao B., Luo B., Wei Q., Adaptive dynamic programming for control: A survey and recent advances, IEEE Transactions on Systems, Man, and Cybernetics: Systems 51 (1) (2021) 142–160.
[29]
Lopez V.G., Lewis F.L., Dynamic multiobjective control for continuous-time systems using reinforcement learning, IEEE Transactions on Automatic Control 64 (7) (2019) 2869–2874.
[30]
Lopez V.G., Lewis F.L., Wan Y., Liu M., Hewer G., Estabridis K., Stability and robustness analysis of minmax solutions for differential graphical games, Automatica 121 (2020).
[31]
Odekunle A., Gao W., Davari M., Jiang Z.-P., Reinforcement learning and non-zero-sum game output regulation for multi-player linear uncertain systems, Automatica 112 (2020).
[32]
Rizvi S.A.A., Lin Z., Output feedback adaptive dynamic programming for linear differential zero-sum games, Automatica 122 (2020).
[33]
Sassano M., Astolfi A., Combining Pontryagin’s principle and dynamic programming for linear and nonlinear systems, IEEE Transactions on Automatic Control 65 (12) (2020) 5312–5327.
[34]
Vamvoudakis K.G., Fotiadis F., Kanellopoulos A., Kokolakis N.-M.T., Nonequilibrium dynamical games: A control systems perspective, Annual Reviews in Control 53 (2022) 6–18.
[35]
Vamvoudakis K.G., Hespanha J.P., Cooperative Q-learning for rejection of persistent adversarial inputs in networked linear quadratic systems, IEEE Transactions on Automatic Control 63 (4) (2018) 1018–1031.
[36]
Vamvoudakis K.G., Modares H., Kiumarsi B., Lewis F.L., Game theory-based control system algorithms with real-time reinforcement learning: How to solve multiplayer games online, IEEE Control Systems Magazine 37 (1) (2017) 33–52.
[37]
Vrabie D., Lewis F.L., Adaptive dynamic programming for online solution of a zero-sum differential game, Journal of Control Theory and Applications 9 (3) (2011) 353–360.
[38]
Wu C., Li X., Pan W., Liu J., Wu L., Zero-sum game-based optimal secure control under actuator attacks, IEEE Transactions on Automatic Control 66 (8) (2021) 3773–3780.
[39]
Wu H.-N., Luo B., Simultaneous policy update algorithms for learning the solution of linear continuous-time H ∞ state feedback control, Information Sciences 222 (2013) 472–485.
[40]
Zhao J., Yang C., Dai W., Gao W., Reinforcement learning-based composite optimal operational control of industrial systems with multiple unit devices, IEEE Transactions on Industrial Informatics 18 (2) (2022) 1091–1101.
[41]
Zhao J., Yang C., Gao W., Modares H., Chen X., Dai W., Linear quadratic tracking control of unknown systems: A two-phase reinforcement learning method, Automatica 148 (2023).
[42]
Zhao J., Yang C., Gao W., Zhou L., Reinforcement learning and optimal control of PMSM speed servo system, IEEE Transactions on Industrial Electronics 70 (8) (2023) 8305–8313.
[43]
Zhou K., Doyle J.C., Glover K., Robust and optimal control, Prentice Hall, Upper Saddle River, NJ, 1996.
[44]
Zhou Y., Vamvoudakis K.G., Haddad W.M., Jiang Z.-P., A secure control learning framework for cyber-physical systems under sensor and actuator attacks, IEEE Transactions on Cybernetics 51 (9) (2021) 4648–4660.
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Published In
Automatica (Journal of IFAC) Volume 163, Issue C
May 2024
520 pages
ISSN:0005-1098
Issue’s Table of Contents
Copyright © 2024.
Publisher
Pergamon Press, Inc.
United States
Publication History
Published: 09 July 2024
Author Tags
- Policy iteration
- Zero-sum games
- Game algebraic Riccati equations
- Adaptive dynamic programming
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- Rapid-communication
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