Optimal Impulsive Control Problems Motivated by Mechanical Systems With Vibrations and Blockable DOFs

Abstract

We consider singular optimal control problems stated for differential-algebraic measure-driven equations. The latter take the form of complementarity systems, which admit jumps of state trajectories produced by open-loop and state-conditioned impulses, acting independently. As an inspiration for the addressed class of models, we turn to mechanical systems driven by time-dependent holonomic (shock impacts, control vibrations) and/or nonholonomic (impactive blocking/releasing system's degrees of freedom) constraints. For our problems, we adapt an approach based on singular space-time transformation. This approach involves approximation of discontinuous solutions of the impulsive complementarity system by ordinary, physically meaningful control processes. Since the complexity of the addressed problems is too high for the analytical investigation, we focus on their numerical investigation, and propose a general computational method.