Data driven stability analysis of black-box switched linear systems
Data driven stability analysis of black-box switched linear systems
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DOI：
10.1016/j.automatica.2019.108533
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发表时间：
2018-03
期刊：
影响因子：
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通讯作者：
Joris Kenanian;Ayca Balkan;R. Jungers;P. Tabuada
中科院分区：
文献类型：
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作者：
Joris Kenanian;Ayca Balkan;R. Jungers;P. Tabuada
我们能从有限数目的轨迹快照的知识中得出未知动力系统的稳定性吗？我们解决了切换线性系统的这个黑盒问题。我们证明了，对于任意给定的随机观测集，可以给出概率稳定性保证。这些担保的概率性质意味着它们的质量和所需的信心水平之间存在权衡。我们提供了一种计算最佳稳定性保证的显式方法，它是观测次数和所需置信度的函数。我们的证明技术依赖于几何分析、机会约束优化和切换系统的稳定性分析工具，包括联合谱半径。
Can we conclude the stability of an unknown dynamical system from the knowledge of a finite number of snapshots of trajectories? We tackle this black-box problem for switched linear systems. We show that, for any given random set of observations, one can give probabilistic stability guarantees. The probabilistic nature of these guarantees implies a trade-off between their quality and the desired level of confidence. We provide an explicit way of computing the best stability-like guarantee, as a function of both the number of observations and the required level of confidence. Our proof techniques rely on geometrical analysis, chance-constrained optimization, and stability analysis tools for switched systems, including the joint spectral radius.