Skip to Main content Skip to Navigation
Journal articles

Optimal control of infinite-dimensional piecewise deterministic Markov processes and application to the control of neuronal dynamics via Optogenetics

Abstract : In this paper we define an infinite-dimensional controlled piecewise deterministic Markov process (PDMP) and we study an optimal control problem with finite time horizon and unbounded cost. This process is a coupling between a continuous time Markov Chain and a set of semilinear parabolic partial differential equations, both processes depending on the control. We apply dynamic programming to the embedded Markov decision process to obtain existence of optimal relaxed controls and we give some sufficient conditions ensuring the existence of an optimal ordinary control. This study, which constitutes an extension of controlled PDMPs to infinite dimension, is motivated by the control that provides Optogenetics on neuron models such as the Hodgkin-Huxley model. We define an infinite-dimensional controlled Hodgkin-Huxley model as an infinite-dimensional controlled piecewise deterministic Markov process and apply the previous results to prove the existence of optimal ordinary controls for a tracking problem.
Complete list of metadatas

Cited literature [52 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01320498
Contributor : Vincent Renault <>
Submitted on : Monday, May 23, 2016 - 11:54:45 PM
Last modification on : Friday, March 27, 2020 - 3:30:28 AM

File

Preprint_PDMP.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01320498, version 1

Citation

Vincent Renault, Michèle Thieullen, Emmanuel Trélat. Optimal control of infinite-dimensional piecewise deterministic Markov processes and application to the control of neuronal dynamics via Optogenetics. Networks and Heterogeneous Media, AIMS-American Institute of Mathematical Sciences, 2017, 12 (3), pp.417--459. ⟨hal-01320498⟩

Share

Metrics

Record views

652

Files downloads

369