On the Nonuniqueness and Instability of Solutions of Tracking-Type Optimal Control Problems

Constantin Christof; Dominik Hafemeyer

paper

On the Nonuniqueness and Instability of Solutions of Tracking-Type Optimal Control Problems

arXiv:2007.08250

Abstract

We study tracking-type optimal control problems that involve a non-affine, weak-to-weak continuous control-to-state mapping, a desired state $y_{d}$ , and a desired control $u_{d}$ . It is proved that such problems are always nonuniquely solvable for certain choices of the tuple $(y_{d}, u_{d})$ and instable in the sense that the set of solutions (interpreted as a multivalued function of $(y_{d}, u_{d})$ ) does not admit a continuous selection.

11 pages