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arXiv · 1906.02250

Optimal control of infinite-dimensional Piecewise Deterministic Markov Processes: a BSDE approach. Application to the control of an excitable cell membrane

Elena Bandini·Michele Thieullen
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Abstract

In this paper we consider the optimal control of Hilbert space-valued infinite-dimensional Piecewise Deterministic Markov Processes (PDMP) and we prove that the corresponding value function can be represented via a Feynman-Kac type formula through the solution of a constrained Backward Stochastic Differential Equation. A fundamental step consists in showing that the corresponding integro-differential Hamilton-Jacobi-Bellman equation has a unique viscosity solution, by proving a suitable comparison theorem. We apply our results to the control of a PDMP Hodgkin-Huxley model with spatial component, previously studied in [22], [21] and inspired by optogenetics.

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Elena Bandini, Michele Thieullen. 2019-06-05. Optimal control of infinite-dimensional Piecewise Deterministic Markov Processes: a BSDE approach. Application to the control of an excitable cell membrane. https://arxiv.org/abs/1906.02250

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