On the Optimal Speed Problem for the Class of Linear Autonomous Infinite-Dimensional Discrete-Time Systems with Bounded Control and Degenerate Operator

Abstract

The optimal speed problem for the class of linear discrete-time systems with the infinite-dimensional state vector and degenerate operator is solved. Some properties of convex sets are formulated and proved. Necessary and sufficient conditions under which this problem has a solution in the case of the zero point located on the boundary of the reachability set are established. The optimality conditions are written as a discrete-time maximum principle. For the inner points, the degenerate character of the maximum principle is demonstrated. For an inner point, the optimal speed problem is solved by developing an algorithm with reduction to the admissible case of the boundary point. Some examples are given.