Set membership identification of switched linear systems with known number of subsystems
Set membership identification of switched linear systems with known number of subsystems
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DOI：
10.1016/j.automatica.2014.10.101
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发表时间：
2015-01-01
期刊：
影响因子：
6.4
通讯作者：
Sznaier, Mario
中科院分区：
文献类型：
--
作者：
Ozay, Necmiye;Lagoa, Constantino;Sznaier, Mario
本文解决了在集合成员框架中鲁棒识别一类离散时间线性混合系统（切换线性模型）的问题。给定来自噪声过程的输入/输出数据的有限集合，目标是双重的：（i）确定该数据是否由在先验已知数量的子系统之间切换的系统生成，以及（ii）在这种情况下识别一组合适的线性模型以及可以解释可用实验信息的a切换序列。我们的主要结果表明，这些问题相当于最小化一个矩阵的秩，该矩阵的条目在优化变量中是仿射的，受到凸约束的约束，这些变量是具有有限支持的（未知）Borel 测度的矩。使用众所周知的（紧）凸松弛秩可以进一步将问题简化为可以有效解决的半定优化。在本文的第二部分中，我们扩展这些结果来处理导致输入/输出测量损坏的传感器故障。假设这些失败很少发生，我们表明该问题可以重新转换为一种优化形式，其目标是同时最小化矩阵的秩和第二个矩阵的非零行数。在这两种情况下，利用众所周知的凸松弛秩和稀疏性会导致可以有效解决的整体半定优化问题。这些结果通过多个示例进行说明，显示在存在噪声和传感器故障的情况下识别性能得到显着提高。 (C) 2014 Elsevier Ltd. 保留所有权利。
This paper addresses the problem of robust identification of a class of discrete-time linear hybrid systems, switched linear models, in a set membership framework. Given a finite collection of input/output data from a noisy process the objective is twofold: (i) establish whether this data was generated by a system that switches amongst an a priori known number of subsystems, and (ii) in that case identify a suitable set of linear models along with a-switching sequence that can explain the available experimental information. Our main result shows that these problems are equivalent to minimizing the rank of a matrix whose entries are affine in the optimization variables, subject to a convex constraint imposing that these variables are the moments of an (unknown) Borel measure with finite support. The use of well known (tight) convex relaxations of rank allows for further reducing the problem to a semidefinite optimization that can be efficiently solved. In the second part of the paper we extend these results to handle sensor failures that result in corrupted input/output measurements. Assuming that these failures are infrequent, we show that the problem can be recast into an optimization form where the objective is to simultaneously minimize the rank of a matrix and the number of nonzero rows of a second one. In both cases, appealing to well known convex relaxations of rank and sparsity leads to overall semidefinite optimization problems that can be efficiently solved. These results are illustrated with multiple examples showing substantially improved identification performance in the presence of noise and sensor faults. (C) 2014 Elsevier Ltd. All rights reserved.