The solution of finite‐time optimal control problems with control time delays

Abstract

AbstractThe design of deterministic LQP optimal control systems is considered for plants with control delays and a finite optimization interval. First, a solution is obtained to the fixed end‐point optimal control problem. An expression for the open‐loop optimal control is derived in the s‐domain. The closed‐loop optimal time‐varying gain matrix is then calculated from the s‐domain results. The open‐loop and closed‐loop solutions to the free end‐point optimal control problem are also given. The constant gain, infinite‐time, feedback control law is obtained as a limiting case of these results.The receding‐horizon optimal control problem for plants with control signal delays is also considered. The solution to this problem yields a constant feedback gain matrix which has obvious advantages for implementation. This gain matrix is not the same as the constant solution to the infinite‐time problem. The receding‐horizon control laws are derived for both the fixed and free end‐point problems, and these are shown to produce asymptotically stable closed‐loop systems.