| Abstract: | The 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. |
