Approximate dynamic programming for two-player zero-sum game related to H ∞ control of unknown nonlinear continuous-time systems

International Journal of Control, Automation and Systems

Volumn 13, Issue 1, 2015, Pages 99-109

  Yasini, Sholeh ^a   Sistani, Mohammad Bagher Naghibi ^a   Karimpour, Ali ^a  

^a FERDOWSI UNIVERSITY OF MASHHAD   (Iran)

Author keywords

Approximate dynamic programming, concurrent learning; H control; neural networks; two player zero sum game; unknown dynamics

Indexed keywords

CONCURRENCY CONTROL; CONTINUOUS TIME SYSTEMS; GAME THEORY; LEARNING ALGORITHMS; NEURAL NETWORKS; NONLINEAR CONTROL SYSTEMS; SYSTEM THEORY;

ALGORITHM FOR SOLVING; APPROXIMATE DYNAMIC PROGRAMMING; HAMILTON-JACOBI-ISAACS; NEURAL NETWORK (NN); NONLINEAR CONTINUOUS-TIME SYSTEMS; OPTIMAL VALUE FUNCTIONS; PERSISTENCY OF EXCITATION; ZERO-SUM GAME;

DYNAMIC PROGRAMMING;

EID: 84925507657     PISSN: 15986446     EISSN: 20054092     Source Type: Journal    
DOI: 10.1007/s12555-014-0085-5     Document Type: Article

References (31)

1. K. Zhou and J. C. Doyle, Essentials of Robust Control, Prentice-Hall,1997.
2. ∞ control,” IEEE Trans. on Automatic Control, vol. 37, no. 6, pp. 770–784, June 1992.
3. ∞Optimal Control and Related Minmax Design Problem, Boston, MA: Birkhäuser, 1995.
4. R. Beard and T. McLain, “Successive Galerkin approximation algorithms for nonlinear optimal and robust control,” International Journal of Control, vol. 71, no. 5, pp. 717–743, 1998.
5. ∞ control method for bilinear systems,” International Journal of Control, Automation, and Systems, vol. 1, no. 2, pp. 171–177, June 2003.
6. ∞ controller design for a class of uncertain linear systems with actuator failures,” International Journal of Control, Automation, and Systems, vol. 6, no. 6, pp. 954–959, December 2008.
7. M. Abu-Khalaf, F. L. Lewis, and J. Huang, “Neurodynamic programming and zero-sum games for constrained control systems,” IEEE Trans. on Neural Networks, vol. 19, no. 7, pp. 1243–1252, July 2008.
8. D. Shen and J. B. Cruz Jr, “Disturbance attenuation analysis of state feedback Nash strategy for two-player linear quadratic sequential games,” International Journal of Control, Automation, and Systems, vol. 7, no. 6, pp. 905–910, December 2009.
9. ∞ control for nonlinear uncertain stochastic T-S fuzzy systems with time delays,” Applied Mathematics Letters, vol. 24, no. 12, pp. 1986–1994, December 2011.
10. ∞ control for uncertain stochastic T-S fuzzy systems with discrete interval and distributed time-varying delays,” International Journal of Automation and Computing, vol. 10, no. 1, pp. 18–31, February 2013.
11. P. J. Werbos, “Approximate dynamic programming for real-time control and neural modeling,” in Handbook of Intelligent Control, D. A. White and D. A. Sofge eds. Brentwood U.K.: Multiscience Press, 1992.
12. D. P. Bertsekas and J. N. Tsitsiklis, Neuro-dynamic Programming, Athena Scientific, MA, 1996.
13. F. L. Lewis, D. Vrabie, and K. Vamvoudakis, “Reinforcement learning and feedback control: using natural decision methods to design optimal adaptive controllers,” IEEE Control Systems Magazine, vol. 32, no. 6, pp. 76–105, December 2012.
14. M. Sharma and A. Verma, “Wavelet reduced order observer based adaptive tracking control for a class of uncertain nonlinear systems using reinforcement learning,” International Journal of Control, Automation, and Systems, vol. 11, no. 3, pp. 496–502, June 2013.
15. D. Vrabie and F. L. Lewis, “Neural network approach to continuous time direct adaptive optimal control for partially unknown nonlinear systems,” Neural Networks, vol. 22, no. 3, pp. 237–246, April 2009.
16. K. Vamvoudakis and F. L. Lewis, “Online actorcritic algorithm to solve the continuous infinite time horizon optimal control problem,” Automatica, vol. 46, no. 5, pp. 878–888, May 2010.
17. H. Modares, M. B. Naghibi Sistani, and F. L. Lewis, “A policy iteration approach to online optimal control of continuous-time constrained-input systems,” ISA Transactions, vol. 52, no. 5, pp. 611–621, September 2013.
18. S. Bhasin, R. Kamalapurkar, M. Johnson, K. Vamvoudakis, F. L. Lewis, and D. Dixon, “A novel actor-critic-identifier architecture for approximate optimal control of uncertain nonlinear systems,” Automatica, vol. 59, no. 1, pp. 82–92, January 2013.
19. D. Vrabie and F. L. Lewis, “Adaptive dynamic programming for online solution of a zero-sum differential game,” Journal of Control Theory and Applications, vol. 9, no. 3, pp. 353–360, July 2011.
20. K. Vamvoudakis and F. L. Lewis, “Online solution of nonlinear two-player zero-sum games using synchronous policy iteration,” International Journal of Robust and Nonlinear Control, vol. 22, no. 13, pp. 1460–1483, September 2012.
21. ∞ control of constrained input systems,” International Journal of Adaptive Control and Signal Processing, vol. 28, no. 3–5, pp. 232–254, March-May 2014.
22. T. Dierks and S. Jagannathan, “Optimal control of affine nonlinear continuous-time systems using an online Hamilton-Jacobi-Isaacs formulation,” Proc. of the 49th Conf. Decision and Control, pp. 3048–3053, 2010.
23. ∞ control,” IEEE Trans. on Neural Networks and Learning Systems, vol. 23, no. 12, pp. 1884–1895, December 2012.
24. M Johnson, S. Bhasin, and D. Dixon, “Nonlinear two-player zero-sum game approximate solution using a policy iteration algorithm,” Proc. of the Conf. Decision and Control, pp. 142–147, 2011.
25. H. Modares, F. L. Lewis, and M. B. Naghibi Sistani, “Adaptive optimal control of unknown constrained-input systems using policy iteration and neural networks,” IEEE Trans. on Neural Networks and Learning Systems, vol. 24, no. 10, pp. 1513–1525, October 2013.
26. R. Kamalapurkar, P. Walters, and W. Dixon, “Concurrent learning-based approximate optimal regulation,” Proc. of the Conf. Decision and Control, pp. 6256–6261, 2013.
27. H. Modares, F. L. Lewis, M. B. Naghibi Sistani, G. Chowdhary, and T. Yucelen, “Adaptive optimal control for the partially-unknown constrained-input using policy iteration with experience replay,” Proc. of the Conf. AIAA Guidance, Navigation, and Control, pp. 1–11, 2013.
28. H. Modares, F. L. Lewis, and M. B. Naghibi Sistani, “Integral reinforcement learning and experience replay for adaptive optimal control of partially- unknown constrained-input continuous-time systems,” Automatica, vol. 50, no. 1, pp. 193–202, January 2014.
29. F. L. Lewis, D. Vrabie, and V. Syrmos, Optimal Control, 3rd edition, Wiley, 2012.
30. K. Hornik, M. Stinchcombe, and H. White, “Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks,” Neural Networks, vol. 3, no. 5, pp. 551–560, 1990.
31. F. L. Lewis, S. Jagannathan, and A. Yesildirek, Neural Network Control of Robot Manipulators and Nonlinear Systems, Taylor & Francis, New York, NY, USA, 1999.