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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS: Vol. 132, No. 2, pp. 307320, February 2007 ( 2007) DOI: 10.1007/s10957-006-9131-7
G. Y. TANG2 AND Y. D. ZHAO3
Communicated by Q. C. Zhao
Published Online: 7 February 2007
Abstract. This paper is concerned with the optimal control of a class of nonlinear time-delay systems affected by external persistent disturbances. A feedforward and feedback optimal control (FFOC) law, consisting of analytical linear feedforward and feedback terms and the limit of a compensation sequence, is obtained by a successive approximation approach (SAA). In order to obtain a physically realizable feedforward control, a disturbance observer is introduced in the exosystem. Simulation results demonstrate the validity of the SAA and the robustness of the FFOC.
Key Words. Nonlinear time-delay systems, successive approximation approach, optimal control, feedforward control, disturbance observer.
1. Introduction
Almost all practical systems are inherently nonlinear. The difculty of the optimal control for nonlinear systems is solving nonlinear two-point boundary-value (TPBV) problems according to the maximum principle or the Hamilton-Jacobi-Bellman (HJB) equations obtained by applying the dynamic programming approach. In fact, analytical solutions of nonlinear TPBV problems or the HJB equations do not exist generally, with the exception of the simplest cases. Many contributions have focused on an approximation based on solving a state-dependent Riccati equation (Refs. 13). Recently, Tang proposes a new successive approximate approach based on solving a sequence of linear inhomogeneous vector differential equations (Ref. 4). This approach requires only solving a sequence
1 This work was supported by the National Natural Science Foundation of China, Grant 60574023 and the Natural Science Foundation of Qingdao City of China, Grant 05-1-JC-94.
2 Professor, College of Information Science and Engineering, Ocean University of China, Qingdao, China; e-mail: [email protected].
3 PhD Candidate, College of Information Science and Engineering, Ocean University of China, Qingdao, China; e-mail: [email protected].
307 0022-3239/07/0200-0307/0 2007 Springer Science+Business Media, Inc.
Optimal Control of Nonlinear Time-Delay Systems with Persistent Disturbances1
308 JOTA: VOL. 132, NO. 2, FEBRUARY 2007
of linear vector differential equations, instead of a sequence of Riccati matrix differential equations indicated in Refs. 13. Banks and McCaffrey proposed a universal theory which gives general results on solutions of nonlinear differential equations (Ref. 5). The approximation theory has been applied to solving the control-afne nonlinear optimal control...