Stochastic Extremum Seeking in the Presence of Constraints

Authors:	Coito Fernando, Universidade Nova de Lisboa, Portugal Lemos João, INESC ID-Lisboa, Portugal Alves Sebastião, Instituto Superior Técnico -Universidade Técnica de Lisboa, Portugal
Topic:	1.2 Adaptive and Learning Systems
Session:	Adaptive and Learning Approaches to Controller Design
Keywords:	Adaptive control; constraint satisfaction; optimal search techniques; convergence analysis; singular perturbation method

Abstract

The problem of adaptive minimization of globally unknown functions under constraints on the independent variable is considered in a stochastic framework. The main contribution of this paper consists in the extension of the CAM algorithm to vector problems. By resorting to the ODE analysis for analyzing stochastic algorithms and singular perturbation methods, it is shown that the only possible convergence points in the vector case are the constrained local minima. Simulations for dimension 2 problems illustrate this result.