Closed-loop Solution to Optimal Control for Discrete-Time Systems with Final State Constraints

This paper is concerned with the linear quadratic (LQ) control problem of discrete-time systems with terminal state constraints. Firstly, lagrange multiplier is used to convert the final constraints into parts of cost function. Secondly, on the basis of the maximum principle, the solvability condition is presented to guarantee the existence of the optimum solution and then the corresponding optimal feedback controller is designed. An illustrate example is provided to demonstrate the effectiveness of the methods proposed in this paper.