Online solution of nonlinear two-player zero-sum games using synchronous policy iteration

International Journal of Robust and Nonlinear Control

Volumn 22, Issue 13, 2012, Pages 1460-1483

  Vamvoudakis, Kyriakos G ^a   Lewis, F L ^a  

^a UNIVERSITY OF TEXAS AT ARLINGTON   (United States)

Author keywords

approximate dynamic programming; Hamilton Jacobi Isaacs equation; Nash equilibrium; synchronous zero sum game policy iteration

Indexed keywords

ADAPTIVE LEARNING ALGORITHM; APPROXIMATE DYNAMIC PROGRAMMING; CLOSED LOOP STABILITY; COMPLEX NONLINEAR SYSTEM; CONTINUOUS TIME; GAME POLICIES; GAME PROBLEM; HAMILTON-JACOBI-ISAACS; HAMILTON-JACOBI-ISAACS EQUATIONS; INFINITE HORIZONS; NASH EQUILIBRIA; ON-LINE GAMING; OPTIMAL VALUE FUNCTIONS; OPTIMAL VALUES; PERSISTENCE OF EXCITATION; POLICY ITERATION; REAL TIME; SADDLE POINT; SIMULATION EXAMPLE; TUNING ALGORITHM; ZERO-SUM GAME;

ADAPTIVE ALGORITHMS; CONTINUOUS TIME SYSTEMS; LEARNING ALGORITHMS; LINEAR SYSTEMS; NONLINEAR SYSTEMS; OPTIMAL SYSTEMS; ROBUST CONTROL;

GAME THEORY;

EID: 84864463039     PISSN: 10498923     EISSN: 10991239     Source Type: Journal    
DOI: 10.1002/rnc.1760     Document Type: Article

References (34)

1. Tijs S,. 2003. Introduction to Game Theory, Hindustan Book Agency: India.
2. Başar T, Olsder GJ,. 1999. Dynamic Noncooperative Game Theory (Classic in Applied Mathematics 23) (2nd edn), SIAM: Philadelphia, PA.
3. ∞ Optimal Control and Related Minimax Design Problems, Birkhäuser: Boston, MA.
4. ∞, control. IEEE Transactions on Automatic Control. 1992 37 6: 770-784.
5. Doya K,. Reinforcement learning in continuous time and space. Neural Computation. 2000 12 1: 219-245.
6. Doya K, Kimura H, Kawato M,. Neural mechanisms of learning and control. IEEE Control Systems Magazine. 2001 21 4: 42-54.
7. Howard RA,. 1960. Dynamic Programming and Markov Processes, MIT Press: Cambridge, MA.
8. Si J, Barto A, Powel W, Wunch D,. 2004. Handbook of Learning and Approximate Dynamic Programming, John Wiley: Hoboken, NJ.
9. Sutton RS, Barto A G,. 1998. Reinforcement Learning: An Introduction, MIT Press: Cambridge, MA.
10. Vrabie D, Vamvoudakis K, Lewis F,. Adaptive optimal controllers based on generalized policy iteration in a continuous-time framework, Proceedings of the IEEE Mediterranean Conference on Control and Automation. Thessaloniki, Greece, June 2009; 1402-1409.
11. Bertsekas DP, Tsitsiklis JN,. 1996. Neuro-Dynamic Programming, Athena Scientific: Belmont, MA.
12. Werbos PJ,. 1974. Beyond regression: new tools for prediction and analysis in the behavior sciences, Ph.D. Thesis, Harvard University.
13. Werbos PJ,. 1992. Approximate dynamic programming for real-time control and neural modeling, In Handbook of Intelligent Control, White DA, Sofge DA, (eds), Van Nostrand Reinhold, New York.
14. Vrabie D,. 2009. Online adaptive optimal control for continuous time systems, Ph.D. Thesis, Department of Electrical Engineering, University of Texas at Arlington, Arlington, TX.
15. Vamvoudakis KG, Lewis FL,. Online actor-critic algorithm to solve the continuous-time inifinite horizon optimal control problem. Automatica. 2010 46 5: 878-888.
16. Lewis FL, Syrmos VL,. 1995. Optimal Control, John Wiley: New York.
17. ∞-control. Journal of Mathematical Systems, Estimation, and Control. 1996 6 1: 1-22.
18. Bardi M, Capuzzo-Dolcetta I,. 1997. Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, Birkhäuser: Boston, MA.
19. ∞ control. Automatica. 2009 45 4: 881-888.
20. Abu-Khalaf M, Lewis FL,. Neurodynamic programming and zero-sum games for constrained control systems. IEEE Transactions on Neural Networks. 2008 19 7: 1243-1252.
21. ∞ state feedback control with input saturation. IEEE Transactions on Automatic Control. 2006 51 12: 1989-1995. (Pubitemid 46002295)
22. Kleinman D,. On an iterative technique for Riccati equation computations. IEEE Transactions on Automatic Control. 1968 13 1: 114-115.
23. Adams R, Fournier J,. 2003. Sobolev Spaces, Academic Press: New York.
24. Abu-Khalaf M, Lewis FL,. Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach. Automatica. 2005 41 5: 779-791. (Pubitemid 40352391)
25. Finlayson BA,. 1990. The method of weighted residuals and variational principles, Academic Press: New York.
26. Hornik K, Stinchcombe M, White H,. Universal Approximation of an unknown mapping and its derivatives using multilayer feedforward networks. Neural Networks. 1990 3 5: 551-560.
27. Sandberg EW,. Notes on uniform approximation of time varying systems on finite time intervals. IEEE Transactions on Circuits and Systems 1: Fundamental Theory and Apprications. 1998 45 8: 863-865.
28. Ioannou P, Fidan B,. 2006. Adaptive Control Tutorial (Advances in Design and Control), SIAM: Philidelphia, PA.
29. Tao G,. 2003. Adaptive Control Design and Analysis (Adaptive and Learning Systems for Signal Processing, Communications and Control Series), Wiley-Interscience: Hoboken, NJ.
30. Stevens B, Lewis FL,. 2003. Aircract Control and Simulation (2nd edn), John Wiley: Hoboken, NJ.
31. Nevistic V, Primbs JA,. 1996. Constrained nonlinear optimal control: a converse HJB approach, Technical Report Technical Report 96-021, California Institute of Technology, Pasadena, CA.
32. Lewis FL, Jagannathan S, Yesildirek A,. 1999. Neural Network Control of Robot Manipulators and Nonlinear Systems, Taylor & Francis: Bristol, PA.
33. Khalil HK,. 1996. Nonlinear Systems, Prentice-Hall: Upper Saddle River, NJ.
34. Bhasin S, Johnson M, Dixon WE,. A model free robust policy iteration algorithm for optimal control of nonlinear systems, Proceedings of the 49th IEEE Conference on Decision and Control, Atlanta, GA, 15-17 December 2010; 3060-3065.