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Linearization techniques for controlled piecewise deterministic markov processes; application to zubov's method

机译：用于控制分段确定性马尔可夫过程的线性化技术;在祖波夫方法中的应用

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摘要

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.
机译：我们旨在使用职业测度公式和Zubov方法为受控的分段确定性过程表征吸引域。首先，我们提供了针对PDMP的打折，无限水平控制问题的线性规划（基本和对偶）公式。这些公式涉及一组无限维的概率测度，并使用粘度解理论获得。其次，这些工具允许构造稳定措施，并避免在控制串联的情况下假设稳定。然后将可控制性域的特征描述为相关汉密尔顿-雅各比积分微分方程的便捷解的某个水平集。理论结果适用于与随机基因网络相关的PDMP。对于基因表达的库克模型给出了明确的计算。

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