Global real-time optimization by output-feedback extremum-seeking control with sliding modes

This paper addresses the design of a sliding mode based extremum-seeking controller for a class of single-input-single-output (SISO) uncertain nonlinear systems with unmatched and state-dependent strong nonlinearities. We demonstrate that it is possible to achieve an arbitrarily small neighborhood of the desired optimal point using only output-feedback. The key idea is the combination of a periodic switching function with a norm state observer. As an important advantage, we show that the proposed scheme achieves extremum-seeking for all initial conditions, i.e., the real-time optimization algorithm has global convergence properties. An application to a simple nonderivative optimizer illustrates the viability of the proposed approach.