A proportional-integral extremum-seeking controller design technique

This paper proposes an alternative extremum seeking control design technique for the solution of real-time optimization control problems. The technique considers a proportional-integral approach that minimizes the impact of a time-scale separation on the transient performance of the extremum-seeking controller. It is assumed that the equations describing the dynamics of the nonlinear system and the cost function to be minimized are unknown and that the objective function is measured. The dynamics are assumed to be of relative degree one with respect to the objective function. Two simulation examples are presented to demonstrate the effectiveness of the proposed technique