Convergence of a Reactive Planning Algorithm

Abstract

The reactive planning algorithms proposed by P. Maes in Artificial Intelligence for real-time decision making and other derived algorithms are empirically known to converge, but no mathematical proof has been proposed. The evolution equations of these incremental algorithms can be translated into discrete time non-linear dynamical systems. We prove the convergence of such dynamical systems, provided the necessary assumptions are fulfilled, and we give an expression for the limit.