Quadratic Optimal Control of Linear Complementarity Systems: First-Order Necessary Conditions and Numerical Analysis

This article is dedicated to the analysis of quadratic optimal control of linear complementarity systems (LCSs), which are a class of strongly nonlinear and nonsmooth dynamical systems. Necessary first-order conditions are derived that take the form of an LCS with inequality constraints, hence are numerically tractable. Sufficiency is proved in a specific sense. Numerical examples illustrate the theoretical developments and demonstrate the efficiency of the complementarity approach.