Optimal Control Problems with Vector-Valued Impulse Controls and Time Delays
Optimization and Control
2024-09-02 v1
Abstract
We consider a nonlinear control system with vector-valued measures as controls and with dynamics depending on time delayed states. First, we introduce a notion of discontinuous, bounded variation solution associated with this system and establish an equivalent representation formula for it, inspired by the approach known in delay-free impulsive control as the `graph completions' method. Then, thanks to this equivalent formulation, we prove well-posedness properties of these solutions and also derive necessary optimality conditions in the form of a Maximum Principle for an associated minimization problem.
Cite
@article{arxiv.2408.17342,
title = {Optimal Control Problems with Vector-Valued Impulse Controls and Time Delays},
author = {Giovanni Fusco and Monica Motta and Richard Vinter},
journal= {arXiv preprint arXiv:2408.17342},
year = {2024}
}