Abstract
In this chapter, zero-sum games are investigated for discrete-time systems based on the model-free ADP method. First, an effective data-based optimal control scheme is developed via the iterative ADP algorithm to find the optimal controller of a class of discrete-time zero-sum games for Roesser type 2-D systems. Since the exact models of many 2-D systems cannot be obtained inherently, the iterative ADP method is expected to avoid the requirement of exact system models. Second, a data-based optimal output feedback controller is developed for solving the zero-sum games of a class of discrete-time systems, whose merit is that not only knowledge of the system model is not required, but neither is information of the system states. Theoretical analysis and a simulation study show the validity of the methods presented.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aangenent W, Kostic D, de Jager B, Van de Molengraft R, Steinbuch M (2005) Data-based optimal control. In: Proceedings of American control conference, Portland, pp 1460–1465
Abu-Khalaf M, Lewis FL (2008) Neurodynamic programming and zero-sum games for constrained control systems. IEEE Trans Neural Netw 19:1243–1252
Abu-Khalaf M, Lewis FL, Huang J (2006) Policy iterations on the Hamilton–Jacobi–Isaacs equation for H ∞ state feedback control with input saturation. IEEE Trans Autom Control 51:1989–1995
Al-Tamimi A, Abu-Khalaf M, Lewis FL (2007) Adaptive critic designs for discrete-time zero-sum games with application to H ∞ control. IEEE Trans Syst Man Cybern, Part B, Cybern 37:240–247
Al-Tamimi A, Lewis FL, Abu-Khalaf M (2007) Model-free q-learning designs for linear discrete-time zero-sum games with application to H ∞ control. Automatica 43:473–481
Al-Tamimi A, Lewis FL, Abu-Khalaf M (2007) Model-free Q-learning designs for linear discrete-time zero-sum games with application to H-infinity control. Automatica 43:473–481
Basar T, Bernhard P (1995) H ∞ optimal control and related minimax design problems. Birkhauser, Basel
Basar T, Olsder GJ (1982) Dynamic noncooperative game theory. Academic Press, New York
Bertsekas DP (2003) Convex analysis and optimization. Athena Scientific, Boston
Cui LL, Zhang HG, Zhang X, Luo YH (2011) Adaptive critic design based output feedback control for discrete-time zero-sum games. In: Proceedings of IEEE symposium on adaptive dynamic programming and reinforcement learning, France, pp 190–195
Hua X, Mizukami K (1994) Linear-quadratic zero-sum differential games for generalized state space systems. IEEE Trans Autom Control 39:143–147
Li CJ, Fadali MS (1991) Optimal control of 2-D systems. IEEE Trans Autom Control 36:223–228
Luenberger DG (1969) Optimization by vector space methods. Wiley, New York
Tsai JS, Li JS, Shieh LS (2002) Discretized quadratic optimal control for continuous-time two-dimensional systems. IEEE Trans Circuits Syst I, Fundam Theory Appl 49:116–125
Uetake Y (1992) Optimal smoothing for noncausal 2-D systems based on a descriptor model. IEEE Trans Autom Control 37:1840–1845
Wei QL, Zhang HG, Cui LL (2009) Data-based optimal control for discrete-time zero-sum games of 2-D systems using adaptive critic designs. Acta Autom Sin 35:682–692
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag London
About this chapter
Cite this chapter
Zhang, H., Liu, D., Luo, Y., Wang, D. (2013). Zero-Sum Games for Discrete-Time Systems Based on Model-Free ADP. In: Adaptive Dynamic Programming for Control. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-4757-2_8
Download citation
DOI: https://doi.org/10.1007/978-1-4471-4757-2_8
Publisher Name: Springer, London
Print ISBN: 978-1-4471-4756-5
Online ISBN: 978-1-4471-4757-2
eBook Packages: EngineeringEngineering (R0)