Optimal Control of Nonconvex Discrete and Differential Inclusions

Optimization problems for discrete and diierential inclusions have many important applications and generalize both standard and nonstandard models in optimal control for open-loop and closed-loop control systems. In this paper we consider optimal control problems for dynamic systems governed by such inclusions with general endpoint constraints. We provide a variational analysis of diierential inclusions based on their nite diierence approximations and recent results in nonsmooth analysis. Using these techniques, we obtain reened necessary optimality conditions for nonconvex-valued discrete and diierential inclusions in a general setting. These conditions are expressed in terms of robust nonconvex generalized derivatives for nonsmooth mappings and multifunctions. We also provide a brief survey of recent results in this direction.