Control of Stochastic Hybrid Systems and Its Applications to Systems Biology

本文研究了随机混合系统的最优控制和离散抽象问题。对概率布尔网络的控制也进行了讨论。作为主要研究成果，提出了一种具有概率约束的最优控制问题的求解方法，以及一种有限时间区间内的离散抽象方法。此外，还讨论了基于数值模拟的生物系统的应用。此外，对于概率布尔网络，提出了一种多药物控制方法和一种基于概率模型检查器的验证方法。

In this research, optimal control and discrete abstraction for stochastic hybrid systems have been addressed. Control of probabilistic Boolean networks has also been addressed. As main results, a solution method of the optimal control problem with probabilistic constraints, and a discrete abstraction method in finite time interval have been proposed. In addition, an application to biological systems has also been discussed based on numerical simulations. Furthermore, for a probabilistic Boolean network, a control method under multiple drugs and a verification method using a probabilistic model checker have been proposed.