Stabilizability of Stochastic Linear Systems with Finite Feedback Data Rates
Stabilizability of Stochastic Linear Systems with Finite Feedback Data Rates
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DOI：
10.1137/s0363012902402116
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发表时间：
2004-02
期刊：
影响因子：
--
通讯作者：
G. Nair;R. Evans
中科院分区：
文献类型：
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作者：
G. Nair;R. Evans
有限数据速率反馈控制是一个新兴的领域，它结合了控制和信息理论的思想。它提出的一个基本问题是，在给定的动态系统不可能通过任何编码和控制律稳定之前，闭环数据速率可以有多低。类似于信源编码，这定义了足以实现“可靠”控制的最小无差错数据速率，并且对于没有干扰的线性时不变系统，已经推导出了它的显式表达式。在本文中，更一般的情况下，有限维线性系统的过程和观测噪声被认为是均方状态稳定性的目标。利用信息论中的熵权不等式和一个新的量化误差界，在初始状态和噪声概率分布很弱的条件下，通过归纳论证，导出了下确界稳定数据速率的显式表达式.
Feedback control with limited data rates is an emerging area which incorporates ideas from both control and information theory. A fundamental question it poses is how low the closed-loop data rate can be made before a given dynamical system is impossible to stabilize by any coding and control law. Analogously to source coding, this defines the smallest error-free data rate sufficient to achieve "reliable" control, and explicit expressions for it have been derived for linear time-invariant systems without disturbances. In this paper, the more general case of finite-dimensional linear systems with process and observation noise is considered, the object being mean square state stability. By inductive arguments employing the entropy power inequality of information theory, and a new quantizer error bound, an explicit expression for the infimum stabilizing data rate is derived, under very mild conditions on the initial state and noise probability distributions.