Optimal Control Applications and Methods, Vol. 17, pp. 29-43, 1996.

In this paper we propose an approach to solving infinite planning-horizon, quadratic-optimal, regulator problems with linear, static, state feedback for nonlinear discrete-time systems. The approach is based on solving a sequence of approximate problems constructed by combining a finite-horizon problem with an infinite-horizon, linear problem. A gradient-flow algorithm is derived to solve the approximate problems. As part of this, a new algorithm is derived for computing the gradient of the cost functional, based on a system of difference equations to be solved completely forward in time. Two numerical examples are presented.

KEY WORDS: optimal control; infinite, planning horizon; approximate problems; gradient flow.