A time-varying extremum-seeking control approach for discrete-time systems

• This paper considers the solution of a real-time optimization problem for a class of unknown discrete-time nonlinear systems.
• The main contribution of the paper is to formulate the extremum-seeking problem as a time-varying discrete-time estimation problem.
• The approach is shown to minimize the impact of the choice of dither signals on the performance of the control system.
• A novel application of extremum-seeking control for model-predictive control.

This paper considers the solution of a real-time optimization problem using adaptive extremum seeking control for a class of unknown discrete-time nonlinear systems. 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 main contribution of the paper is to formulate the extremum-seeking problem as a time-varying discrete-time estimation problem. The proposed approach is shown to avoid the need for averaging results which minimizes the impact of the choice of dither signals on the performance of the extremum seeking control system. Several examples are used to illustrate the effectiveness of the proposed technique.