A proportional integral extremum-seeking control approach for discrete-time nonlinear systems

This paper proposes a proportional-integral extremum-seeking control technique for a class of discrete-time nonlinear dynamical systems with unknown dynamics. The technique is a generalization of existing time-varying extremum-seeking control techniques that provides fast transient performance of the closed-loop system to the optimum equilibrium of a measured objective function. The main contribution of the proposed technique is the addition of a proportional action that can be used to minimize the impact of a time-scale separation on the transient performance of the extremum-seeking control system. The integral action fulfills the role of standard ESC techniques to identify optimal equilibrium conditions. The effectiveness of the proposed approach is demonstrated using a simulation example.