Optimal State Feedback Control of Nonlinear Systems with Time Delays
In this chapter, optimal state feedback control problems of nonlinear systems with time delays are studied. In general, the optimal control for time-delay systems is an infinite-dimensional control problem, which is very difficult to solve and there is presently no good method for dealing with this problem. In this chapter, the optimal state feedback control problems of nonlinear systems with time delays both in states and controls are investigated. By introducing a delay matrix function, the explicit expression of the optimal control function can be obtained. Next, for nonlinear time-delay systems with saturating actuators, we further study the optimal control problem using a nonquadratic functional, where two optimization processes are developed for searching the optimal solutions. The above two results are for the infinite-horizon optimal control problem. To the best of our knowledge, there are no results on the finite-horizon optimal control of nonlinear time-delay systems. Hence, in the last part of this chapter, a novel optimal control strategy is developed to solve the finite-horizon optimal control problem for a class of time-delay systems.