Convex Certificates for Model (In)validation of Switched Affine Systems With Unknown Switches
Convex Certificates for Model (In)validation of Switched Affine Systems With Unknown Switches
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DOI：
10.1109/tac.2014.2351714
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发表时间：
2014-11-01
影响因子：
6.8
通讯作者：
Lagoa, Constantino
中科院分区：
文献类型：
--
作者：
Ozay, Necmiye;Sznaier, Mario;Lagoa, Constantino
检查模型的有效性是系统识别过程中的关键步骤。在处理切换仿射系统时尤其如此，因为在这种情况下，从噪声数据中识别系统的问题通常是 NP-Hard 的，并且只能通过使用启发式和松弛法在实践中解决。因此，在将确定的模型用于控制器设计之前，应根据其他实验数据对它们进行系统验证。在本文中，我们解决了具有未知开关的输出误差形式的多输入多输出切换仿射系统的模型（输入）验证问题。第一步，我们证明可以通过解决一系列凸优化问题来获得必要且充分的失效证书。原则上，这些问题涉及越来越大的矩阵。然而，正如我们在论文中通过利用半代数几何的最新结果所表明的那样，所提出的算法保证在可以根据先验信息显式计算的有限数量的步骤之后停止。此外，该算法利用底层优化问题的稀疏结构来大幅减少计算负担。使用学术示例和计算机视觉中出现的一个重要问题：活动监控来说明所提出方法的有效性。
Checking validity of a model is a crucial step in the process of system identification. This is especially true when dealing with switched affine systems since, in this case, the problem of system identification from noisy data is known to be generically NP-Hard and can only be solved in practice by using heuristics and relaxations. Therefore, before the identified models can be used for instance for controller design, they should be systematically validated against additional experimental data. In this paper we address the problem of model (in) validation for multi-input multi-output switched affine systems in output error form with unknown switches. As a first step, we prove that necessary and sufficient invalidation certificates can be obtained by solving a sequence of convex optimization problems. In principle, these problems involve increasingly large matrices. However, as we show in the paper by exploiting recent results from semialgebraic geometry, the proposed algorithm is guaranteed to stop after a finite number of steps that can be be explicitly computed from the a priori information. In addition, this algorithm exploits the sparse structure of the underlying optimization problem to substantially reduce the computational burden. The effectiveness of the proposed method is illustrated using both academic examples and a non-trivial problem arising in computer vision: activity monitoring.