Abstract
In this chapter, optimal state feedback control problems of nonlinear systems with time delays are studied. In general, the optimal control for time-delay systems is an infinite-dimensional control problem, which is very difficult to solve and there is presently no good method for dealing with this problem. In this chapter, the optimal state feedback control problems of nonlinear systems with time delays both in states and controls are investigated. By introducing a delay matrix function, the explicit expression of the optimal control function can be obtained. Next, for nonlinear time-delay systems with saturating actuators, we further study the optimal control problem using a nonquadratic functional, where two optimization processes are developed for searching the optimal solutions. The above two results are for the infinite-horizon optimal control problem. To the best of our knowledge, there are no results on the finite-horizon optimal control of nonlinear time-delay systems. Hence, in the last part of this chapter, a novel optimal control strategy is developed to solve the finite-horizon optimal control problem for a class of time-delay systems.
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References
Malek-Zavarei M, Jashmidi M (1987) Time-delay systems: analysis, optimization and applications. North-Holland, Amsterdam, pp 80–96
Song RZ, Zhang HG (2011) The finite horizon optimal control for a class of time-delay affine nonlinear system. Neural Comput Appl. doi:10.1007/s00521-011-0706-3
Song RZ, Zhang HG, Wei QL, Luo YH (2010) Optimal control laws for time-delay systems with saturating actuators based on heuristic dynamic programming. Neurocomputing 73:3020–3027
Tong SC, Liu CL, Li YM, Zhang HG (2011) Adaptive fuzzy decentralized control for large-scale nonlinear systems with time-varying delays and unknown high-frequency gain sign. IEEE Trans Syst Man Cybern, Part B, Cybern 41:474–485
Wang ZS, Zhang HG (2010) Global asymptotic stability of reaction–diffusion Cohen–Grossberg neural networks with continuously distributed delays. IEEE Trans Neural Netw 21:39–49
Wang ZS, Zhang HG, Li P (2010) An LMI approach to stability analysis of reaction–diffusion Cohen–Grossberg neural networks concerning Dirichlet boundary conditions and distributed delays. IEEE Trans Syst Man Cybern, Part B, Cybern 40:1596–1606
Wang YC, Zhang HG, Wang XY, Yang DS (2010) Networked synchronization control of coupled dynamic networks with time-varying delay. IEEE Trans Syst Man Cybern, Part B, Cybern 40:1468–1479
Wang FY, Jin N, Liu DR, Wei Q (2011) Adaptive dynamic programming for finite-horizon optimal control of discrete-time nonlinear systems with ϵ-error bound. IEEE Trans Neural Netw 22:24–36
Wei QL, Zhang HG, Liu DR, Zhao Y (2010) An optimal control scheme for a class of discrete-time nonlinear systems with time delays using adaptive dynamic programming. Acta Autom Sin 36:121–129
Zhang HG, Wang YC (2008) Stability analysis of Markovian jumping stochastic Cohen–Grossberg neural networks with mixed time delays. IEEE Trans Neural Netw 19:366–370
Zhang HG, Xie YH, Wang ZL, Zheng CD (2007) Adaptive synchronization between two different chaotic neural networks with time delay. IEEE Trans Neural Netw 18:1841–1845
Zhang HG, Wang ZS, Liu DR (2008) Robust stability analysis for interval Cohen–Grossberg neural networks with unknown time-varying delays. IEEE Trans Neural Netw 19:1942–1955
Zhang HG, Wang YC, Liu DR (2008) Delay-dependent guaranteed cost control for uncertain stochastic fuzzy systems with multiple tire delays. IEEE Trans Syst Man Cybern, Part B, Cybern 38:126–140
Zhang HG, Wei QL, Luo YH (2008) A novel infinite-time optimal tracking control scheme for a class of discrete-time nonlinear systems via the greedy HDP iteration algorithm. IEEE Trans Syst Man Cybern, Part B, Cybern 38:937–942
Zheng CD, Zhang HG, Wang ZS (2009) New delay-dependent global exponential stability criterion for cellular-type neural networks with time-varying delays. IEEE Trans Circuits Syst II, Express Briefs 56:250–254
Zheng CD, Zhang HG, Wang ZS (2010) Improved robust stability criteria for delayed cellular neural networks via the LMI approach. IEEE Trans Circuits Syst II, Express Briefs 57:41–45
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© 2013 Springer-Verlag London
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Zhang, H., Liu, D., Luo, Y., Wang, D. (2013). Optimal State Feedback Control of Nonlinear Systems with Time Delays. In: Adaptive Dynamic Programming for Control. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-4757-2_4
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DOI: https://doi.org/10.1007/978-1-4471-4757-2_4
Publisher Name: Springer, London
Print ISBN: 978-1-4471-4756-5
Online ISBN: 978-1-4471-4757-2
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