Work

Optimal Control Problems with Vector-Valued Impulse Controls and Time Delays

Year: 2025

Type: article

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 concept 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 completion’ 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 optimization problem.

Source: Journal of Optimization Theory and Applications

DOI: 10.1007/s10957-025-02845-8

Authors: Giovanni Fusco, Monica Motta, Richard Vinter

Institutions: Louisiana State University, University of Padua, Imperial College London

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni