A utopic multi-objective extremum-seeking controller design technique

This paper considers the solution of a multi-objective optimization problem using adaptive extremum seeking control for a class of uncertain nonlinear systems. It is assumed that the equations describing the dynamics of the nonlinear system and the cost functions to be optimized are unknown and that the objective functions are measured. 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. The technique guarantees convergence of the system to specific desirable Pareto solutions using a utopic formulation. A simulation example is used to illustrate the effectiveness of the proposed technique.