Robust integral sliding mode controller for optimisation of measurable cost functions with constraints

This paper proposes an online constrained extremum-seeking approach for an unknown convex function with unknown constraints within a class of uncertain dynamical systems with an available output disturbed by a stochastic noise. It is assumed that the objective function along with the constraints are available for measurement. The main contribution of the paper is the formulation of the problem using the penalty method and the development of an extremum seeking algorithm based on a modified synchronous detection method for computing a stochastic gradient descent procedure. In order to reject the undesirable uncertainties and perturbations of the dynamic plant from the beginning of the process, we employ the standard deterministic Integral Sliding Mode Control transforming the initial dynamic plant to static one. Then, we apply the gradient decedent technique. We consider time varying parameters of the suggested procedure for compensating the unknown dynamics. To validate the exposition, we perform a numerical example simulation.