Synthesis of Optimal Dynamic Quantizers for Discrete-Valued Input Control
Synthesis of Optimal Dynamic Quantizers for Discrete-Valued Input Control
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DOI：
10.1109/tac.2008.929400
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发表时间：
2008-10-01
影响因子：
6.8
通讯作者：
Sugie, Toshiharu
中科院分区：
文献类型：
--
作者：
Azuma, Shun-ichi;Sugie, Toshiharu
本文提出了一种用于控制离散输入线性定常系统的最优动态量化器综合方法。这里考虑的量化器包括动态反馈机制，我们找到量化器参数，使得由给定的线性植物和量化器组成的系统是线性植物的输入输出关系的最佳近似。首先，分析了任意给定的动态量化器的性能，推导出性能的封闭形式表达式。基于这个结果，它表明，量化器的设计是减少到一个非凸优化问题，它是很难得到一个解决方案，在一个直接的方式。然而，我们得到一个全局最优解，利用一个特殊的结构的问题，使我们能够放松原来的非凸问题。所得到的问题是很容易解决的，所以我们提供了一个基于线性规划的设计方法，并推导出动态量化器的最佳结构。最后通过数值算例验证了该方法的有效性。
This paper presents an optimal dynamic quantizer synthesis method for controlling linear time-invariant systems with discrete-valued input. The quantizers considered here include dynamic feedback mechanism, for which we find quantizer parameters such that the system composed of a given linear plant and the quantizer is an optimal approximation of the linear plant in terms of the input-output relation. First, the performance of an arbitrarily given dynamic quantizer is analyzed, where we derive a closed form expression of the performance. Based on this result, it is shown that the quantizer design is reduced to a nonconvex optimization problem for which it is hard to obtain a solution in a direct way. We obtain a globally optimal solution, however, by taking advantage of a special structure of the problem which allows us to relax the original nonconvex problem. The resulting problem is easy to solve, so we provide a design method based on linear programming and derive an optimal structure of the dynamic quantizers. Finally, the validity of the proposed method is demonstrated by numerical examples.