Fast Extremum Seeking Control for a Class of Generalized Hammerstein Systems with the Knowledge of Relative Degree

This work extends the existing fast extremum seeking control (ESC) for a class of Hammerstein systems to a class of generalized Hammerstein systems, in which the nonlinear affine dynamical system is connected directly after a given cost function. With the relative degree information of the unknown nonlinear dynamics, a new output is generated. The mapping between the new output and the input has two parts. The first part is proportional to the cost function and the second part is related to the state. By inserting a fast dither signal, the proposed ESC can seek the optimum of this cost function without time-scale separation. Our main results show that with proper selection of tuning parameters, this scheme can achieve arbitrarily fast semi-global practical asymptotic (SPA) convergence. Simulation results support the theoretical findings.