Optimal control of sliding mode processes: A general approach

This paper addresses a general theoretical framework of optimal control problems (OCPs) associated with the conventional sliding mode dynamics. We deal with a class of constrained OCPs governed by nonlinear affine control systems and propose some numerically stable approximations to the sophisticated dynamical optimization problem. The above-mentioned structure of the state equations makes it also possible to consider some sensitivity properties of the optimal solutions. The mathematical approach based on the set-valued analysis allows to study the usual discontinuous sliding mode-type dynamics in the abstract setting and to obtain some general analytical results. These facts can be effectively applied to wide classes of OCPs governed by sliding mode processes and variable structure systems (VSSs).