Closed-Loop Expression of Fixed-end-point LQ Optimal Control for Digital Systems

Abstract

This paper discusses the fixed-end-point linear-quadratic optimal control problem for a multi-input linear time-invariant discrete-time system. Using the general form of the inputs which satisfy the zero-end-point condition, the fixed-end-point problem is transformed into the new free-end-point problem and the special deadbeat control. The optimal inputs are made up of three phases, and they are expressed by the variable gain state feedback and the special deadbeat control. The variable gains are obtained by the special nonstationary Riccati equations, and all gains do not depend on the initial state.