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Linear quadratic optimal control problem of stochastic switching systems

The stochastic optimal control problem of linear switching systems with quadratic cost function is investigated. The contribution of this paper is to present a necessary and sufficient condition of optimality for considered switching systems. | Journal of Automation and Control Engineering Vol. 4, No. 6, December 2016 Linear Quadratic Optimal Control Problem of Stochastic Switching Systems Charkaz A. Aghayeva Department of Industrial Engineering, Anadolu University, Eskisehir, Turkey ANAS/Institute of Control Systems, Baku, Azerbaijan Email: cherkez.agayeva@gmail.com Abstract—Switched systems have numerous applications in control of real systems as mechanical systems, automotive industry, aircraft and air traffic control, switching power converters, and many other fields. Optimal control problems of switching systems require the decision of both the optimal solutions and switching sequences. The stochastic optimal control problem of linear switching systems with quadratic cost function is investigated. The contribution of this paper is to present a necessary and sufficient condition of optimality for considered switching systems. condition of optimality for stochastic linear switching systems is obtained in section III. In section IV, the unique optimal control is derived in terms of state feedback via the solution of Riccati equation. The paper is concluded in section V with some possible developments and enlargements. Index Terms—condition of optimality, quadratic function, optimal control, switching system constant, R II. In this section we fix notation and definition used throughout this paper. Let N be some positive I. space, . n denotes the n - dimensional real vector denotes the Euclidean norm and , denotes scalar product in R n . E represents expectation ; the set INTRODUCTION of integer numbers 1, ,s is denoted by 1, s ; ' (the prime) denotes derivative; * is the matrix transposition operation. Let wt1 , wt2 ,.,wts are independent Wiener processes, The optimal control problem for linear systems was solved, as well as the filtering one, in 1960s by Kalman [1], but there exist a lot of invariant and non-invariant linear systems with still open optimal control problem. There