Gradient-Based Approach to Solve Optimal Periodic Output Feedback Control Problems

We discuss the numerical solution of the output feedback optimal periodic control problem by using a gradient search based optimization approach. Extension of this approach to the simultaneous stabilization of periodic multimodels is also considered. For the evaluation of function and its gradient explicit expressions are derived which involve the numerical solution of a pair of discrete-time periodic Lyapunov equations. Numerically reliable algorithms based on the periodic Schur decomposition are used for the efficient solution of these equations. A satellite positioning example illustrates the effectiveness of the presented approach to solve a practical periodic control problem. ∗A short version of this paper has been presented at the CACSD’96 Symp., Dearborn, MI, Sept. 15-18, 1996 †The authors are with DLR Oberpfaffenhofen, German Aerospace Research Establishment, Institute of Robotics and System Dynamics, P.O.B. 1116, D-82230 Wessling, Germany;Phone: +49-8153-282408, Fax:+498153-1441, E-mail: [email protected].