Discrete-Time Linear Quadratic Optimal Control with Fixed and Free Terminal State via Double Generating Functions

Abstract

A double generating functions based method for the discrete-time linear quadratic optimal control problem with fixed and free terminal state, i.e., hard constraint problem and soft constraint problem, is developed in this paper. By this method, the optimal state and input can be expressed by functions only in terms of the boundary conditions and pre-computed coefficients. Accordingly, the whole optimal computation can be divided into two parts in which the off-line part calculates the coefficients and the on-line part generates the optimal solutions by these proposed functions. In view of this, the developed method is useful in the on-line iterative computation for optimal control problem with a number of different boundary conditions. Examples demonstrate the effectiveness of the double generating functions method for the both hard and soft constraint problems with different boundary conditions.