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

Giovanni Fusco (), Monica Motta () and Richard Vinter ()
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Giovanni Fusco: Louisiana State University
Monica Motta: University of Padova
Richard Vinter: Imperial College London

Journal of Optimization Theory and Applications, 2026, vol. 208, issue 1, No 24, 33 pages

Abstract: 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.

Keywords: Impulse Control; Time Delay Systems; Optimal Control; Maximum Principle; Bounded Variation; 49N25; 93C43; 49K21; 26A45; 49J21 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/s10957-025-02845-8

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