Finite-Horizon Linear-Quadratic Optimal Control of Discrete-Time Systems with Input Delay

The paper addresses the problem of remote plant regulation with the use of linear-quadratic (LQ) optimal control strategy. Since modern, practical applications favor digital solutions, the controller design is conducted directly in discrete time domain. By direct treatment of Riccati equation, it is shown that the finite-time optimization problem for systems involving delay may be reduced to an equivalent delay-free problem with variables expressed in delay compensator dynamics and time-varying control gains. As a result, the computational complexity to solve the design equations is reduced to that encountered in direct plant control and efficient implementation is ensured.