A GRADIENT FLOW APPROACH TO COMPUTING A NONLINEAR DISCRETE-TIME QUADRATIC OPTIMAL FEEDBACK GAIN MATRIX

In this paper we propose an approach to solving infinite planning hori zon quadratic optimal regulator problems with linear static state feed back for discrete time systems. The approach is based on solving a seq uence of approximate problems constructed by combining a finite horizo n problem with an infinite horizon linear problem. A gradient-flow alg orithm is derived to solve the approximate problems. As part of this, a new algorithm is derived for computing the gradient of the cost func tional, based on a system of difference equations to be solved complet ely forward in time. Two numerical examples are presented.