Global optimization of three-input systems using multi-unit extremum seeking control

An efficient global optimization method based on multi-unit extremum seeking has been proposed recently for scalar and two-input systems. For scalar systems, the global optimum is obtained by controlling the finite-difference gradient and reducing the offset used for calculating this gradient. With two inputs, the uni-variate method is repeated on the circumference of a circle of reducing radius. In this paper, the concept is extended to three-input systems where the circle of varying radius sits on a shrinking sphere. The theoretical concepts are illustrated on the global optimization of several examples. The results show the capability of the proposed technique in deterministic convergence to the global optimum of the three-input systems.