“Stage-by-stage201D; optimization approach to optimal control for general time-delay systems

In this paper, parallel to the well-known dynamic programming for delay free systems, we develop a stage-by-stage optimization approach to LQ control for systems with multiple delays in both input and state by introducing an associated dual backward stochastic systems and applying inner-product theory. The obtained results show us that: (1) The controller design for time delay systems is in fact the estimator design for different signals from the dual stochastic time delay systems; (2) The calculation of the optimal control for general time delay systems is related with Riccati-type partial difference equation; (3) The optimal control problem for time delay systems and the problem for delay- free systems can be solved in a unified form.