Finite time stochastic stability and the analysis of tracking systems
Finite time stochastic stability and the analysis of tracking systems
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DOI：
10.1109/tac.1966.1098315
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发表时间：
1966-04
影响因子：
6.8
通讯作者：
H. Kushner
中科院分区：
文献类型：
--
作者：
H. Kushner
给出了一个求概率P_{x}{\sup_{T\geq t\geq 0} V（X_{t}）\geq\lambda}的上界的Liapunov类方法，其中x_{0} = x，xt是具有离散或连续参数的Markov过程，V（\cdot）是某个函数.这种估计是许多跟踪、控制和可靠性研究中最感兴趣的量。该方法涉及找到合适的（随机）李雅普诺夫函数。其结果也是有限时间随机稳定性的结果。这些定理是在Dynkin [1]的一些定理的基础上发展起来的。给出了几个说明性的例子。
A (Liapunov-like) method is presented for obtaining upper bounds of the probability P_{x}{\sup_{T\geq t\geq 0} V(X_{t})\geq\lambda} , where x_{0} = x and x t is a Markov process with either discrete or continuous parameter, and V(\cdot) is some function. Such estimates are the quantity of greatest interest in numerous tracking, control, and reliability studies. The method involves finding suitable (stochastic) Liapunov functions. The results are also results in (what may be termed) finite-time stochastic stability. The theorems are based on some theorems of Dynkin [1]. Several illustrative examples are given.