Relaxing the Optimality Condition in Receding Horizon Control

Ali Jadbabie and John Hauser
Submitted, 2000 Conference on Decision and Control

Receding horizon control is based on iteratively solving an open-loop finite horizon optimization problem. Despite its success in a variety of industrial applications, theoretical issues such as stability were not completely addressed until recently. It was shown in previous work that by utilizing a suitable Control Lyapunov Function (CLF) as terminal cost, the stability of the receding horizon scheme can be guaranteed and the region of attraction of the receding horizon controller can be estimated. The key point in this approach, which made it different from others, was removal of additional stability constraints, hence making the optimizations much easier to solve. A requirement implied in the previous results was being able to solve the optimizations globally. In this paper, that assumption is removed and it is shown that the optimality can be replaced by an improvement property. A numerical example using the inverted pendulum is presented to illustrate this point.

Conference Paper (postscript)