The objective of this paper is to study the stochastic version of a previous paper of the authors, in which hybrid control for deterministic systems was considered. The modelling is quite similar to the deterministic case. We have a system whose state is composed of a continuous part and a discrete part. They are affected by a continuous type control and an impulse control. The dynamics is moreover perturbed by noise, also a continuous and a discrete noise process. The Markovian character of the state process is preserved. We develop the model and show how the dynamic programming approach leads to some involved quasi-variational inequality.
Numerical Analysis and Computation | Probability
A. Bensoussan and J.-L. Menaldi, Stochastic hybrid control, Journal of Mathematical Analysis and Applications, 249 (2000), 261-288. doi: 10.1006/jmaa.2000.7102