Optimal Control of Nonconvex Differential Inclusions.
Optimization problems for discrete and differential 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 differential inclusions based on their finite difference approximations and recent results in nonsmooth analysis. Using these techniques, we obtain refined necessary optimality conditions for nonconvex-valued discrete and differential 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.
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