Noncausal Optimal Tracking of Linear Switched Systems
In this paper we consider the noncausal optimal tracking problem on the finite time interval for linear switched systems. We consider the problem to obtain the solution of both optimal switching sequences and optimal control inputs such that the tracking
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Abstract. In this paper we consider the noncausal optimal tracking problem on the finite time interval for linear switched systems. We consider the problem to obtain the solution of both optimal switching sequences and optimal control inputs such that the tracking error is minimized. In this paper we assume that information of reference signals is known a priori for the whole time interval and utilize its information so that the tracking performace becomes better. We study a computation method of the optimal performance including some information of tracking errors and present an iterative algorithm to determine the optimal timing and optimal tracking performance numerically. Keywords: Switched systems; Optimal control; GSLQ problems; Noncausal tracking theory; Riccati equations.
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Introduction
On optimal control problems for switched systems, the problem to obtain the solution of both the optimal switching sequences and the optimal inputs is very important, and so much works have been done by many researchers recently ([1,2,6,19,20,22]). In particular, X. Xu and P. J. Antsaklis have studied the optimal timing and control problem by the parametrization approach([19,22]). They have decomposed the problem into two stages. In the first stage, they have considered a cost optimization problem over fixed switching sequences. In the second stage, they have considered a nonlinear optimization problem to find local switching sequences. In order to solve these two problems, they have presented an algorithm based on the gradient projection method and its variations([3]). For linear qudratic (LQ) problem, they have constructed the optimization algorithm by using the general Riccati equation parametrized by switching instants. The embedded control system theory is a more general control theory than the theory by their time parametrization approach for the switched systems. The switched systems can be ”embedded” into a larger class of systems. Recently the relationship between the switched and embedded systems has been researched([2]). M. Egerstedt and B. Mishra (Eds.): HSCC 2008, LNCS 4981, pp. 372–385, 2008. c Springer-Verlag Berlin Heidelberg 2008
Noncausal Optimal Tracking of Linear Switched Systems
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It is well known that, for design of tracking control systems, preview information of reference signals is very useful for improving the performance of the closed-loop systems, and much work has been done for preview control systems([4,5,7,8,9,10,11,12,13,14,15,16,17,18]). U. Shaked and C. E. de Souza have presented the H∞ tracking theory with preview by a game theoretic approach ([17]). Their theory can be restricted to optimal tracking theory and also extended to robust H∞ tracking control theory([18]) or stochastic H∞ tracking control theory([7,8,9]). Their theory has been applied to various types of systems, for example, continuous-time systems([8,17,18]), discrete-time systems([4,7]), impulsive systems ([13,14,15,16]) and so on. In this paper we describe that their tracking theory can be applied to the switched syst
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