Extremum seeking control via sliding mode and periodic switching function applied to Raman optical amplifiers

In a recent paper, the authors have proposed an extremum-seeking control strategy to single-input-single-output (SISO) uncertain nonlinear systems. Such proposed sliding mode based real-time optimization algorithm guaranteed global convergence properties to a small neighborhood of the optimal point by means of a periodic switching function. In this paper, we generalize our previous results to a multivariable framework and applies this new controller to the optimization of the output signal power spectrum of Raman optical amplifiers. The aim is to minimize the output signal power ripple and the deviation of the output signal power from a desired level, considering eventual inclusions/exclusions of signals in the fiber. The convergence analysis is developed in the presence of uncertainties and the control performance is evaluated via numerical simulations.