On Concepts of Controllability for Deterministic and Stochastic Systems
On Concepts of Controllability for Deterministic and Stochastic Systems
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DOI：
10.1137/s036301299732184x
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发表时间：
1999-09
影响因子：
2.2
通讯作者：
A. Bashirov;N. Mahmudov
中科院分区：
文献类型：
--
作者：
A. Bashirov;N. Mahmudov
分别给出了确定性线性平稳控制系统完全可控和近似可控的新的充要条件，这些充要条件是由涉及可控性算子的负解的算子序列的收敛性表述出来的。应用这些条件研究了随机系统的S-可控性（在状态空间中每个点以任意接近1的概率获得任意小邻域的性质）和C-可控性（具有一定均匀性的S-可控性）。证明了具有加性高斯白噪声干扰的部分可观测线性平稳控制系统在所有区间[0，T]上对t>的S—可控性（C—可控性）等价于其确定性部分在所有区间[0，T]上对t>的近似（完全）可控性。
The new necessary and sufficient conditions, which are formulated in terms of convergence of a certain sequence of operators involving the resolvent of the negative of the controllability operator, are found for deterministic linear stationary control systems to be completely and approximately controllable, respectively. These conditions are applied to study the S-controllability (a property of attaining an arbitrarily small neighborhood of each point in the state space with a probability arbitrarily close to one) and C--controllability (the S--controllability fortified with some uniformity) of stochastic systems. It is shown that the S--controllability (the C--controllability) of a partially observable linear stationary control system with an additive Gaussian white noise disturbance on all the intervals [0,T] for T>0 is equivalent to the approximate (complete) controllability of its deterministic part on all the intervals [0,T] for T>0.