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

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