Linearization Techniques for Controlled Piecewise Deterministic Markov Processes; Application to Zubov's Method

Journal Article · Mon Oct 15 00:00:00 EDT 2012 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-012-9169-X· OSTI ID:22092059

Goreac, Dan ^[1]; Serea, Oana-Silvia ^[2]

---

1. Universite Paris-Est, LAMA, UMR8050 (France)
2. Univ. Perpignan Via Domitia, Laboratoire de Matheematiques et PhySique (France)

We aim at characterizing domains of attraction for controlled piecewise deterministic processes using an occupational measure formulation and Zubov's approach. Firstly, we provide linear programming (primal and dual) formulations of discounted, infinite horizon control problems for PDMPs. These formulations involve an infinite-dimensional set of probability measures and are obtained using viscosity solutions theory. Secondly, these tools allow to construct stabilizing measures and to avoid the assumption of stability under concatenation for controls. The domain of controllability is then characterized as some level set of a convenient solution of the associated Hamilton-Jacobi integral-differential equation. The theoretical results are applied to PDMPs associated to stochastic gene networks. Explicit computations are given for Cook's model for gene expression.

• OSTI ID: 22092059
• Journal Information: Applied Mathematics and Optimization, Vol. 66, Issue 2; Other Information: Copyright (c) 2012 Springer Science+Business Media, LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
CONTROL THEORY
HAMILTON-JACOBI EQUATIONS
INTEGRO-DIFFERENTIAL EQUATIONS
LINEAR PROGRAMMING
MARKOV PROCESS
MATHEMATICAL SOLUTIONS
PROBABILITY