论文标题
关于离散时间随机控制系统的职业措施集的收敛，并应用于平均混合系统
On convergence of occupational measures sets of a discrete-time stochastic control system, with applications to averaging of hybrid systems
论文作者
论文摘要
在本文的第一部分中，我们考虑一个离散的随机控制系统。我们表明，在某些条件下，系统对照轨迹产生的一组随机职业措施以及其数学期望集合（因为时间范围倾向于无穷大）与凸面和紧凑型（非随机）集合在一起，这与系统的静止概率集合在一起。在第二部分中，我们应用第一部分获得的结果来处理连续发展并经历某些参数突然变化的混合系统。我们表明，这种混合系统的解由差分包含的解决方案近似，其右侧是由极限职业度量集，其存在和凸的定义，其右侧是在本文的第一部分中确定的。
In the first part of the paper, we consider a discrete-time stochastic control system. We show that, under certain conditions, the set of random occupational measures generated by the state-control trajectories of the system as well as the set of their mathematical expectations converge (as the time horizon tends to infinity) to a convex and compact (non-random) set, which is shown to coincide with the set of stationary probabilities of the system. In the second part, we apply the results obtained in the first part to deal with a hybrid system that evolves in continuous time and is subjected to abrupt changes of certain parameters. We show that the solutions of such a hybrid system are approximated by the solutions of a differential inclusion, the right-hand side of which is defined by the limit occupational measures set, the existence and convexity of which is established in the first part of the paper.
