Multivariable Sliding Mode-based Extremum Seeking Control via Periodic Switching Function and Cyclic Search

In this paper, a new multivariable extremum seeking control approach based on sliding mode and cyclic search for static nonlinear maps is proposed. Classical and even similar methods are characterized by slow convergence rates and local or semi-global convergence/stability properties. Whereas the proposed approach guarantees global and fast convergence to a neighborhood of the extremum of the objective function, because (1) it does not employ averaging and singular perturbation analysis tools and (2) in the control law, a sliding manifold with integral action is designed, which allows the output rapidly to track the reference signal regardless of recurrent changes of the searching direction. Stability and convergence properties are demonstrated using non-linear systems’ analysis tools. Furthermore, a rigorous analysis of the residual oscillations around the extremum is carried out. Numerical simulations are performed to illustrate the theoretical results and highlight the advantages of the proposed strategy in terms of robustness, fast convergence and small residual errors.