The design and performance analysis of multivariate fractional-order gradient-based extremum seeking approach

In this paper, a novel multivariate fractional-order (FO) Gradient-based extremum seeking control (Gradient-based ESC) approach is developed for the optimization of multivariable dynamical systems. The proposed Gradient-based ESC, utilizing FO operators, is presented to not only speed up the convergence rate and enhance the control accuracy but also improve the search efficiency of the extrema by regulating the fractional-order. For multivariable dynamical systems, the stability analysis of the proposed multivariate FO Gradient-based ESC is presented in details to guarantee the convergence performance of multi-input optimization problems. Simulation and experimental results are given to demonstrate the effectiveness and advantages of the proposed approach by comparing with the corresponding integer-order (IO) Gradient-based ESC.