随机系统停留时间的域递归和概率分析及域瞄准控制
Domain Recurrence and Probabilistic Analysis of Residence Time of Stochastic Systems and Domain Aiming Control
摘要：
研究了受控随机非线性系统的区域目标控制问题。这个问题涉及到所得到的闭环随机系统的解的正则性。首先，利用一个Lyapunov型函数证明了具有局部Lipschitz系数的随机微分方程解的存在唯一性定理.给出了一类随机微分方程解不正则的一个基于Lyapunov的充分条件。引入了随机非线性系统的区域常返和停留时间的概念，给出了关于有界开区域和无界区域常返和不常返的各种判据。此外，上界的期望值或矩母函数的停留时间的推导。特别是，平均停留时间和一个狄利克雷问题之间的连接进行了研究，并说明了一个数值例子。最后，研究了一类非线性和线性随机系统的区域目标控制问题。最后给出了几个例子来说明理论结果。
英文摘要：
The problem of domain aiming control is formulated for controlled stochastic nonlinear systems. This issue involves regularity of the solution to the resulting closed-loop stochastic system. To begin with, an extended existence and uniqueness theorem for stochastic differential equation with local Lipschitz coefficients is proven by using a Lyapunov-type function. A Lyapunov-based sufficient condition is also given under which there is no regularity of the solution for a class of stochastic differential equations. The notions of domain recurrence and residence time for stochastic nonlinear systems are introduced, and various criteria for the recurrence and non-recurrence relative to a bounded open domain or an unbounded domain are provided. Furthermore, upper bounds of either the expectation or the moment-generating function of the residence time are derived. In particular, a connection between the mean residence time and a Dirichlet problem is investigated and illustrated with a numerical example. Finally, the problem of domain aiming control is considered for certain types of nonlinear and linear stochastic systems. Several examples are provided to illustrate the theoretical results.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
