2004/05/12 by S. A. Belbas, Belbas, S. A., W. H. Schmidt +2
Engineering · Mathematics · #34K45 #45DO5 #49K15 #49K22 #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Differential Equations Analysis #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations #math.OC #msc:34K45 #msc:45DO5 #msc:49K15 #msc:49K22
paper · pdf · doi:10.48550/arxiv.math/0405207
arxiv created 2004/05/12 · openalex publication_date 2004/05/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider an optimal control problem for a system governed by a Volterra integral equation with impulsive terms. The impulses act on both the state and the control; the control consists of switchings at discrete times. The cost functional includes both, an integrated cost rate (continuous part) and switching costs at the discrete impulse times (discrete part). We prove necessary optimality conditions of a form analogous to a discrete maximum principle. For the particular case of a system governed by impulsive ordinary differential equations, we obtain an impulsive maximum principle as a special case of the necessary optimality conditions for impulsive Volterra equations.