Duality in optimal impulse control

We consider the optimal impulse control of a dynamical system defined by a fixed uncontrolled flow. This problem is associated with two pairs of linear programs for which we prove the solvability and the absence of the duality gaps. Finally, we show how to retrieve the optimal control strategy from the solutions of those linear programs. The theoretical issues are illustrated by the meaningful example on the controlled epidemic model. Crown Copyright (c) 2021 Published by Elsevier Inc. All rights reserved.