Optimal control of difference, differential, and differential-difference inclusions
The paper deals with optimal control problems for differential and differential-difference inclusions with nonconvex admissible velocity sets, the cost being a function depending on initial and terminal states satisfying given constraints. Necessary optimality conditions are presented under suitable conditions. The author derives well-posed discrete approximations with appropriate convergence results, studies optimal solutions for the corresponding finite-dimensional problems and then obtains optimality conditions for the original problem in infinite dimensions by passing to the limit in approximations. The main complications come from dynamic constraints and its finite-difference approximations that lead to an increasing number of (nonsmooth and nonconvex) geometric constraints in corresponding finite-dimensional problems. The author presents basic results of generalized differentiation that allows to handle such situations and supports limiting procedures.
differential and differential-difference inclusions
scientific article; zbMATH DE number 1526507
scientific article