An adaptive optimization scheme with satisfactory transient performance

Abstract

Adaptive optimization (AO) schemes based on stochastic approximation principles such as the Random Directions Kiefer–Wolfowitz (RDKW), the Simultaneous Perturbation Stochastic Approximation (SPSA) and the Adaptive Fine-Tuning (AFT) algorithms possess the serious disadvantage of not guaranteeing satisfactory transient behavior due to their requirement for using random or random-like perturbations of the parameter vector. The use of random or random-like perturbations may lead to particularly large values of the objective function, which may result to severe poor performance or stability problems when these methods are applied to closed-loop controller optimization applications. In this paper, we introduce and analyze a new algorithm for alleviating this problem. Mathematical analysis establishes satisfactory transient performance and convergence of the proposed scheme under a general set of assumptions. Application of the proposed scheme to the adaptive optimization of a large-scale, complex control system demonstrates the efficiency of the proposed scheme.