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

arXiv: https://arxiv.org/abs/2007.08250 · HTML: https://mlsanity.com/paper/2007.08250/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jul 2020.

## Built on by (most cited first, 2 of 2)

- [Turnpike in optimal control of PDEs, ResNets, and beyond](https://mlsanity.com/paper/2202.04097/) (2022)
- [On the Omnipresence of Spurious Local Minima in Certain Neural Network Training Problems](https://mlsanity.com/paper/2202.12262/) (2022)

## Abstract (arXiv)

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.