A Minmax Extremum-Seeking Controller Design Technique

This paper considers the solution of a minmax optimization problem using adaptive extremum seeking control. 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 appropriate selection of the minimizing and the maximizing inputs is also assumed to be known a priori. The proposed extremum-seeking control technique uses a time-varying estimation of the unknown gradients that minimizes the impact of the choice of dither signal on the performance of the extremum seeking control system. Two examples are used to illustrate the effectiveness of the proposed technique.