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A multi-objective extremum-seeking controller design technique. (English) Zbl 1328.93111

Summary: This paper considers the solution of a multi-objective optimisation 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 optimised 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 minimises 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 any point of the set of Pareto optimal solutions. It is adapted to allow the computation of specific desirable Pareto solutions using a utopic formulation. Simulation examples are used to illustrate the effectiveness of the proposed technique.

MSC:

93B51 Design techniques (robust design, computer-aided design, etc.)
90C29 Multi-objective and goal programming
93B40 Computational methods in systems theory (MSC2010)
93C41 Control/observation systems with incomplete information
93C10 Nonlinear systems in control theory
93C15 Control/observation systems governed by ordinary differential equations
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