Robust identification of switched affine systems via moments-based convex optimization
Robust identification of switched affine systems via moments-based convex optimization
复制标题
通过基于矩的凸优化对切换仿射系统进行鲁棒识别
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
M. Sznaier
中科院分区：
文献类型：
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作者：
N. Ozay;C. Lagoa;M. Sznaier
本文解决了在集合成员框架中鲁棒识别一类离散时间仿射混合系统（切换仿射模型）的问题。给定噪声输入/输出数据的有限集合和子系统数量的限制，目标是确定一组合适的仿射模型以及可以解释可用实验信息的切换序列。我们的方法建立在 Vidal 等人提出的代数过程的基础上。用于无噪声测量。在存在范数有界噪声的情况下，这种代数过程会导致非常具有挑战性的非凸多项式优化问题。我们的主要结果表明，这个问题可以简化为最小化矩阵的秩，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）概率分布函数的矩。诉诸众所周知的凸秩松弛会导致可以有效解决的整体半定优化问题。这些结果通过两个示例进行了说明，表明在存在噪声的情况下识别性能得到了显着提高。
This paper addresses the problem of robust identification of a class of discrete-time affine hybrid systems, switched affine models, in a set membership framework. Given a finite collection of noisy input/output data and a bound on the number of subsystems, the objective is to identify a suitable set of affine models along with a switching sequence that can explain the available experimental information. Our method builds upon an algebraic procedure proposed by Vidal et al. for noise free measurements. In the presence of norm bounded noise, this algebraic procedure leads to a very challenging nonconvex polynomial optimization problem. Our main result shows that this problem can be reduced 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) probability distribution function with finite support. Appealing to well known convex relaxations of rank leads to an overall semi-definite optimization problem that can be efficiently solved. These results are illustrated with two examples showing substantially improved identification performance in the presence of noise.