Algebraic Invariance Conditions in the Study of Approximate (Null-)Controllability of Markov Switch Processes

Dan Goreac (1) , Miguel Martinez (2)

1 PS
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We aim at studying approximate null-controllability properties of a particular class of piecewise linear Markov processes (Markovian switch systems). The criteria are given in terms of algebraic invariance and are easily computable. We propose several necessary conditions and a sufficient one. The hierarchy between these conditions is studied via suitable counterexamples. Equivalence criteria are given in abstract form for general dynamics and algebraic form for systems with constant coefficients or continuous switching. The problem is motivated by the study of lysis phenomena in biological organisms and price prediction on spike-driven commodities.

Mots clés: Approximate (null-)controllability; Controlled Piecewise Deterministic Markov Process; Markov switch process; invariance; stochastic gene networks

Domaines: Optimisation et contrôle [math.OC]; Probabilités [math.PR]

Dan Goreac, Miguel Martinez. Algebraic Invariance Conditions in the Study of Approximate (Null-)Controllability of Markov Switch Processes. 2014. ⟨hal-01061543v1⟩