Optimal control for linear time-varying systems with multiple time-delays

This paper considers the optimal control problem of a class of linear time-varying systems with multiple time-delays. A novel design approach to the optimal control law is proposed. By constructing a new state vector, the original system model and the performance index are simplified to equivalent ones without time-delay. So the infinite dimension problem of optimal control for systems with time-delays is avoided. The optimal control law is found by solving a matrix differential equation instead of a two-point boundary value problem, Simulation results demonstrate the effectiveness of the optimal control approach.