A Hybrid Control Algorithm for Gradient-Free Optimization using Conjugate Directions⁎Research partially supported by the European Project "AerIal RoBotic technologies for professiOnal seaRch aNd rescuE" (AirBorne), Call: H2020, ICT-25-2016/17, Grant Agreement no: 780960, by NSF Grants no. ECS-1710621 and CNS-1544396, by AFOSR Grants no. FA9550-16-1-0015, FA9550-19-1-0053, and Grant no. FA9550-19-1-0169, and by CITRIS and the Banatao Institute at the University of California. Issue 2 (2020) - Melis, Alessandro; Sanfelice, Ricardo G.; Marconi, Lorenzo
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.