Optimal dynamic quantizers for discrete-valued input control
Optimal dynamic quantizers for discrete-valued input control
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DOI：
10.1016/j.automatica.2007.06.012
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发表时间：
2008-02-01
期刊：
影响因子：
6.4
通讯作者：
Sugie, Toshiharu
中科院分区：
文献类型：
--
作者：
Azuma, Shun-ichi;Sugie, Toshiharu
本文讨论了一类离散值输入系统（即由离散值输入信号驱动的线性时不变系统）的动态量化器的优化设计问题。这里考虑的量化器采用线性差分方程的形式，为此我们找到一个量化器，使得由给定线性对象和量化器组成的系统在输入输出关系意义上是给定线性对象的最优近似。首先，我们导出一类动态量化器性能的封闭形式表达式。接下来，基于性能分析，给出了最佳的动态量化器及其性能。该结果进一步表明，即使对于这种离散值输入系统，也可以通过现有的线性系统设计工具（例如鲁棒控制理论）轻松设计控制器。最后，讨论了最优动态量化器和另外两个量化器（即后退水平量化器和 Delta Sigma 调制器）之间的关系。 (C) 2007 Elsevier Ltd. 保留所有权利。
This paper discusses an optimal design problem of dynamic quantizers for a class of discrete-valued input systems, i.e., linear time-invariant systems actuated by discrete-valued input signals. The quantizers considered here are in the form of a linear difference equation, for which we find a quantizer such that the system composed of a given linear plant and the quantizer is an optimal approximation of the given linear plant in the sense of the input-output relation. First, we derive a closed form expression for the performance of a class of dynamic quantizers. Next, based on the performance analysis, an optimal dynamic quantizer and its performance are provided. This result further shows that even for such discrete-valued input systems, a controller can be easily designed by the existing tools for the linear system design such as robust control theory. Finally, the relation among the optimal dynamic quantizer and two other quantizers, i.e., the receding horizon quantizer and the Delta Sigma modulator, is discussed. (C) 2007 Elsevier Ltd. All rights reserved.