Abstract
In this chapter, we focus on the design of controllers for continuous-time systems via the ADP approach. Although many ADP methods have been proposed for continuous-time systems, a suitable framework in which the optimal controller can be designed for a class of general unknown continuous-time systems still has not been developed. Therefore, in the first part of this chapter, we develop a new scheme to design the optimal robust tracking controllers for unknown general continuous-time nonlinear systems. The merit of the present method is that we require only the availability of input/output data instead of an exact system model. The obtained control input can be guaranteed to be close to the optimal control input within a small bound. In the second part of this chapter, a novel ADP-based robust neural network controller is developed for a class of continuous-time nonaffine nonlinear systems, which is the first attempt to extend the ADP approach to continuous-time nonaffine nonlinear systems. Numerical simulations have shown that the present methods are effective and can be used for a quite wide class of continuous-time nonlinear systems.
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References
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
Calise AJ, Hovakimyan N, Idan M (2001) Adaptive output feedback control of nonlinear systems using neural networks. Automatica 37:1201–1211
Chellaboina V, Haddad WM (2002) A unification between partial stability and stability theory for time-varying systems. IEEE Control Syst Mag 22:66–75
Cui LL, Luo YH, Zhang HG (2011) Adaptive critic design based robust neural network control for a class of continuous-time nonaffine nonlinear system. In: Proceedings of international conference on modelling, identification and control, Shanghai, pp 26–29
Ge S, Zhang J (2003) Neural-network control of nonaffine nonlinear system with zero dynamics by state and output feedback. IEEE Trans Neural Netw 14:900–918
Hanselmann T, Noakes L, Zaknich A (2007) Continuous-time adaptive critics. IEEE Trans Neural Netw 3:631–647
Khalil HK (2002) Nonlinear system. Prentice Hall, Englewood Cliffs
Kim N, Calise AJ (2007) Several extensions in methods for adaptive output feedback control. IEEE Trans Neural Netw 18:482–494
Kim YH, Lewis FL (2000) Reinforcement adaptive learning neural-net-based friction compensation control for high speed and precision. IEEE Trans Control Syst Technol 8:118–126
Kuljaca O, Lewis FL (2003) Adaptive critic design using non-linear network structure. Int J Adapt Control Signal Prog 17:431–445
Lewis FL, Jagannathan S, Yesildirek A (1999) Neural network control of robot manipulators and nonlinear systems. Taylor & Francis, London
Lin CK (2005) Adaptive critic autopilot design of bank-to-turn missiles using fuzzy basis function networks. IEEE Trans Syst Man Cybern, Part B, Cybern 35:197–206
Lin CK (2009) H ∞ reinforcement learning control of robot manipulators using fuzzy wavelet networks. Fuzzy Sets Syst 160:1765–1786
Liu ZW, Zhang HG, Zhang QL (2010) Novel stability analysis for recurrent neural networks with multiple delays via line integral-type L-K functional. IEEE Trans Neural Netw 21:1710–1718
Murray JJ, Cox CJ, Lendaris GG, Saeks R (2002) Adaptive dynamic programming. IEEE Trans Syst Man Cybern, Part B, Cybern 32:140–153
Rubio JDJ, Yu W (2007) Stability analysis of nonlinear system identification via delayed neural networks. IEEE Trans Circuits Syst II, Express Briefs 54:161–195
Vamvoudakis KG, Lewis FL (2010) Online actor-critic algorithm to solve the continuous-time infinite horizon optimal control problem. Automatica 46:878–888
Vrabie D, Lewis FL (2009) Neural network approach to continuous-time direct adaptive optimal control for partially unknown nonlinear system. Neural Netw 22:237–246
Vrabie D, Pastravanu O, Abu-Khalaf M, Lewis FL (2009) Adaptive optimal control for continuous-time linear systems based on policy iteration. Automatica 45:477–484
Wang ZS, Zhang HG, Yu W (2009) Robust stability of Cohen–Grossberg neural networks via state transmission matrix. IEEE Trans Neural Netw 20:169–174
Wang ZS, Zhang HG, Jiang B (2011) LMI-based approach for global asymptotic stability analysis of recurrent neural networks with various delays and structures. IEEE Trans Neural Netw 22:1032–1045
Zhang HG, Wang ZS, Liu DR (2008) Global asymptotic stability of recurrent neural networks with multiple time-varying delays. IEEE Trans Neural Netw 19:855–873
Zhang HG, Li M, Yang J (2009) Fuzzy model-based robust networked control for a class of nonlinear systems. IEEE Trans Syst Man Cybern, Part A, Syst Hum 39:437–447
Zhang HG, Liu ZW, Huang GB (2010) Novel weighting-delay-based stability criteria for recurrent neural networks with time-varying delay. IEEE Trans Neural Netw 21:91–106
Zhang HG, Cui LL, Zhang X, Luo YH (2011) Data-driven robust approximate optimal tracking control for unknown general nonlinear systems using adaptive dynamic programming method. IEEE Trans Neural Netw 22(12):2226–2236
Zhang HG, Xie XP, Tong SC (2011) Homogeneous polynomially parameter-dependent H ∞ filter designs of discrete-time fuzzy systems. IEEE Trans Syst Man Cybern, Part B, Cybern 41:1313–1322
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Zhang, H., Liu, D., Luo, Y., Wang, D. (2013). Optimal Feedback Control for Continuous-Time Systems via ADP. In: Adaptive Dynamic Programming for Control. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-4757-2_6
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DOI: https://doi.org/10.1007/978-1-4471-4757-2_6
Publisher Name: Springer, London
Print ISBN: 978-1-4471-4756-5
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