Adaptive Dynamic Programming algorithm for finding online the equilibrium solution of the two-player zero-sum differential game

Proceedings of the International Joint Conference on Neural Networks

Volumn , Issue , 2010, Pages

  Vrabie, Draguna ^a   Lewis, Frank ^a  

^a UNIVERSITY OF TEXAS AT ARLINGTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; CONTINUOUS TIME SYSTEMS; DYNAMIC PROGRAMMING; GAME THEORY; RICCATI EQUATIONS;

ADAPTIVE DYNAMIC PROGRAMMING; CONTROL ENGINEERING; DYNAMIC PROGRAMMING ALGORITHM; ENGINEERING COMMUNITY; EQUILIBRIUM SOLUTIONS; INFINITE HORIZONS; LINEAR DYNAMICS; NASH EQUILIBRIA; QUADRATIC COSTS; ZERO-SUM DIFFERENTIAL GAMES;

ITERATIVE METHODS;

EID: 79959444159     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/IJCNN.2010.5596754     Document Type: Conference Paper

References (17)

1. Abu-Khalaf M., Lewis F. L. and Huang J., "Policy Iterations and the Hamilton-Jacobi-Isaacs Equation for H-infinity State Feedback Control with Input Saturation", IEEE Trans. on Automatic Control, 51(12), 2006, pp. 1989-1995.
2. Basar, T., Bernhard, P., H-infinity optimal control and related minimax design problems, Birkhauser, 1995.
3. nd ed., (Classics in Applied Mathematics; 23), SIAM, 1999.
4. Brewer J. W., "Kronecker Products and Matrix Calculus in System Theory", IEEE Trans. on Circuit and System, 25(9), 1978, pp. 772-781.
5. Cherfi, L., Abou-Kandil H., Bourles H., "Iterative method for general algebraic Riccati equation", Proc. ACSE'05, 2005.
6. Damm, T., Rational Matrix Equations in Stochastic Control, Springer-Verlag, Berlin, Germany, 2004.
7. Doyle J., Glover K., Khargonekar P. and Francis B., "State-space solutions to standard H2 and H-infinity control problems", IEEE Trans. Aut. Control, 34, 1989, pp. 831-847
8. Feng Y., Anderson B.D.O., Rotkowitz M: "A game theoretic algorithm to compute local stabilizing solutions to HJBI equations in nonlinear H-infinity control", Automatica, 45(4), 2009, pp. 881-888.
9. 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 Trans. Aut. Control, 53(10), 2008, pp. 2280-2291.
10. Lewis F. L., Syrmos V. L., Optimal Control, John Wiley, 1995.
11. Stoorvogel A. A., The H-infinity Control Problem: A State Space Approach, Prentice-Hall, New York, 1992.
12. Van Der Schaft, A. J., L2-gain analysis of nonlinear systems and nonlinear state feedback H∞ control. IEEE Transactions on Automatic Control, 37(6), 1992, pp. 770-784.
13. D. Vrabie, M. Abu-Khalaf, F.L. Lewis and Y. Wang, "Continuous-time ADP for linear systems with partially unknown dynamics", Proceedings of Symposium on approximate dynamic programming and Reinforcement Learning (ADPRL), Hawaii, USA, April 2007.
14. D. Vrabie, O. Pastravanu, F. Lewis, M. Abu-Khalaf, "Adaptive Optimal Control for Continuous-Time Linear Systems Based on Policy Iteration", Automatica, 45(2), 2009, pp. 477-484.
15. Zhou K. and Khargonekar, P. P., An algebraic Riccati equation approach to H-infinity optimization, Syst. Contr. Lett., 11, 1988, pp. 85-91.
16. Wang Y., Zhou R. and Wen C., "Robust load-frequency controller design for power systems", IEE Proc. C, 140(1), 11-16, 1993.
17. Wei Q. and Zhang H., "A new approach to solve a class of continuous-time nonlinear quadratic zero-sum game using ADP", Proc. IEEE International Conference on Networking, Sensing and Control (ICNSC'08), 6(8) 2008, pp. 507-512.