A Convex Optimization Approach to Synthesizing Bounded Complexity $\ell^{\infty}$ Filters
A Convex Optimization Approach to Synthesizing Bounded Complexity $\ell^{\infty}$ Filters
复制标题
合成有界复杂度$ell^{infty}$过滤器的凸优化方法
DOI：
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发表时间：
2012
影响因子：
6.8
通讯作者：
M. Sznaier
中科院分区：
文献类型：
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作者：
F. Blanchini;M. Sznaier
研究了存在未知有界噪声的最坏情况估计问题。与随机方法相反，这里的目标是将估计误差限制在有界集合内。先前处理该问题的工作表明，基于构造状态一致性集（例如，与先验信息和实验数据一致的所有状态的集合）的估计器的复杂性不能先验地有界，并且原则上可以随时间连续增加。为了避免这个困难，我们提出了一类有界复杂性过滤器，基于限制r长度错误序列（而不是状态）到超矩形的思想。技术说明的主要结果表明，这可以通过使用阶数不大于r的线性时不变滤波器来实现。此外，综合这些滤波器可以简化为凸优化和线搜索的组合。
We consider the worst-case estimation problem in the presence of unknown but bounded noise. Contrary to stochastic approaches, the goal here is to confine the estimation error within a bounded set. Previous work dealing with the problem has shown that the complexity of estimators based upon the idea of constructing the state consistency set (e.g., the set of all states consistent with the a priori information and experimental data) cannot be bounded a priori, and can, in principle, continuously increase with time. To avoid this difficulty we propose a class of bounded complexity filters, based upon the idea of confining r-length error sequences (rather than states) to hyperrectangles. The main result of the technical note shows that this can be accomplished by using linear time invariant filters of order no larger than r. Further, synthesizing these filters reduces to a combination of convex optimization and line search.