Approximation and Numerical Experiments for Control of Time Periodic Parabolic Distributed Parameter Systems

E orts on the numerical approximation and simulation of control of time periodic parabolic distributed parameter system are reported. Test examples have been chosen suc that the optimal control can be explicitly computed via analytical methods. The approximation framework and convergence theory are applied to a polynomial spline based approximation scheme. In the case of control of one dimensional time periodic reaction di usion systems, the convergence of the kernels of the Hilbert-Schmidt representation of the solutions of the approximate periodic Riccati equations is proved. Techniques for solving time periodic Riccati di erential equations and simulation of the optimal feedback control systems are discussed. Numerical results reported here demonstrate the convergence of the approximate control inputs and feedback operators. Numerical simulation is used to investigate the performance of the approximate optimal controls as well as the sensitivity of the closed-loop system to the errors in the time measurements. Research supported in part under a grant from the Air Force O ce of Scienti c Research: AFOSR 90-0091. Center for Applied Mathematical Sciences, Department of Mathematics, University of Southern California, Los Angeles, California, 90089-1113.