Quasi-Newton extremum seeking control based on incremental recursive identification

Abstract

This paper proposes a novel quasi-Newton extremum seeking control method based on incremental recursive identification for a real-time optimization problem. The optimization of static map and dynamical system are both considered where the dynamics of the nonlinear system and the cost function to be minimized are unknown. Firstly, the proposed method only employs the measured function values to effectively estimate the time-varying gradient of the unknown cost function by using incremental recursive least square identification. Then, an extremum seeking control (ESC) approach based on the quasi-Newton direction is developed to improve convergence speed, which only requires the estimated gradient of the objective function without Hessian information. Furthermore, the convergence properties of the proposed ESC method are established for static map and dynamical system. Finally, we demonstrate the superiority and effectiveness of the proposed method using three examples.