A Hybrid Control Algorithm for Gradient-Free Optimization using Conjugate Directions

Abstract

The problem of steering a particular class of n-dimensional continuous-time dynamical systems towards the minima of a function without gradient information is considered. We propose a hybrid controller, implementing a discrete-time Direct Search algorithm based on conjugate directions, able to solve the optimization problem for the resulting closed loop system in an almost global sense. Moreover, we propose a modified version by imposing a lower bound on the step size and able to achieve robust practical convergence to the optimum.