IMPROVING CONVERGENCE OF PERTURBATION-BASED EXTREMUM SEEKING METHODS FOR A CLASS OF DIFFERENTIALLY FLAT SYSTEMS

Perturbation-based extremum-seeking methods require a three level time-scale separation, and so have essentially slow convergence. Intuitively, the convergence can be speeded up using a cascade scheme that accelerates the system dynamics. In this paper, the system under study is assumed to be single-input single-output, flat and the dynamics with respect to the flat output are inverted using feedback linearization. Yet, it is shown here that there exists a residual dynamics between the controlled flat output and the optimized variable which poses an essential limitation. If the dimension of the residual dynamics is less than or equal to one, arbitrary fast convergence with an arbitrary accuracy can be achieved, though this is not the case if the residual dynamics has a higher dimension. Simulation results are used to illustrate the concepts presented in this work.