Abstract
This chapter estimates an off-policy IRL algorithm to obtain the optimal tracking control of the unknown chaotic systems. The performance index function is first given based on the system tracking error and control error. For solving the Hamilton–Jacobi–Bellman (HJB) equation, an off-policy integral reinforcement learning (IRL) algorithm is proposed. It is proven that the iterative control law makes the tracking error system asymptotically stable, and the iterative value function is convergent. Simulation study demonstrates the effectiveness of the developed tracking control method.
References
Gao, S., Dong, H., Sun, X., Ning, B.: Neural adaptive chaotic control with constrained input using state and output feedback. Chin. Phys. B 24(1), 010501 (2015)
Jiang, Y., Jiang, Z.: Computational adaptive optimal control for continuous-time linear systems with completely unknown dynamics. Automatica 48, 2699–2704 (2012)
Lü, J., Chen, G.: A new chaotic attractor coined. Int. J. Bifurc. Chaos 12, 659–661 (2002)
Lü, J., Chen, G., Zhang, S.: Dynamical analysis of a new chaotic attractor. Int. J. Bifurc. Chaos 12, 1001–1015 (2002)
Lü, J., Chen, G., Zhang, S.: The compound structure of a new chaotic attractor. Chaos Solitons Fractals 14, 669–672 (2002)
Lü, J., Lu, J.: Controlling uncertain Lü system using linear feedback. Chaos Solitons and Fractals 17, 127–133 (2003)
Ma, T., Fu, J.: Global exponential synchronization between LĂĽ system and Chen system with unknown parameters and channel time-delay. Chin. Phys. B 20, 050511 (2011)
Ma, T., Zhang, H., Fu, J.: Exponential synchronization of stochastic impulsive perturbed chaotic Lur’e systems with time-varying delay and parametric uncertainty. Chin. Phy. B 17, 4407 (2008)
Murray, J., Cox, C., Lendaris, G., Saeks, R.: Adaptive dynamic programming. IEEE Trans. Syst. Man Cybern. Part C Appl. Rev. 32, 140–153 (2002)
Song, R., Xiao, W., Sun, C., Wei, Q.: Approximation-error-ADP-based optimal tracking control for chaotic systems with convergence proof. Chin. Phys. B 22, 090502 (2013)
Song, R., Xiao, W., Wei, Q.: A new approach of optimal control for a class of continuous-time chaotic systems by an online ADP algorithm. Chin. Phys. B 23, 050504 (2014)
Wei, Q., Liu, D.: Adaptive dynamic programming for optimal tracking control of unknown nonlinear systems with application to coal gasification. IEEE Trans. Autom. Sci. Eng. 11, 1020–1036 (2014)
Wei, Q., Liu, D.: Neural-network-based adaptive optimal tracking control scheme for discrete-time nonlinear systems with approximation errors. Neurocomputing 149, 106–115 (2015)
Wei, Q., Song, R., Sun, Q., Xiao, W.: Off-policy integral reinforcement learning optimal tracking control for continuous-time chaotic systems. Chin. Phys. B 24(9), 090504 (2015)
Xu, C., Wu, Y.: Bifurcation and control of chaos in a chemical system. Appl. Math. Model. (2015, in press)
Yang, D.: Robust networked \(H_{\infty }\) synchronization of nonidentical chaotic Lur’e systems. Chin. Phys. B 23, 010504 (2014)
Zhang, H., Song, R., Wei, Q., Zhang, T.: Optimal tracking control for a class of nonlinear discrete-time systems with time delays based on heuristic dynamic programming. IEEE Trans. Neural Netw. 22, 1851–1862 (2011)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 Science Press, Beijing and Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Wei, Q., Song, R., Li, B., Lin, X. (2018). Off-Policy IRL Optimal Tracking Control for Continuous-Time Chaotic Systems. In: Self-Learning Optimal Control of Nonlinear Systems. Studies in Systems, Decision and Control, vol 103. Springer, Singapore. https://doi.org/10.1007/978-981-10-4080-1_9
Download citation
DOI: https://doi.org/10.1007/978-981-10-4080-1_9
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-4079-5
Online ISBN: 978-981-10-4080-1
eBook Packages: EngineeringEngineering (R0)