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Recent control trends are increasingly relying on communication networks andwireless channels to close the loop for Internet-of-Things applications.Traditionally these approaches are model-based, i.e., assuming a network orchannel model they are focused on stability analysis and appropriate controllerdesigns. However the availability of such wireless channel modeling isfundamentally challenging in practice as channels are typically unknown apriori and only available through data samples. In this work we aim to developalgorithms that rely on channel sample data to determine the stability andperformance of networked control tasks. In this regard our work is the first tocharacterize the amount of channel modeling that is required to answer such aquestion. Specifically we examine how many channel data samples are required inorder to answer with high confidence whether a given networked control systemis stable or not. This analysis is based on the notion of sample complexityfrom the learning literature and is facilitated by concentration inequalities.Moreover we establish a direct relation between the sample complexity and thenetworked system stability margin, i.e., the underlying packet success rate ofthe channel and the spectral radius of the dynamics of the control system. Thisillustrates that it becomes impractical to verify stability under a large rangeof plant and channel configurations. We validate our theoretical results innumerical simulations.

Statistical Learning for Analysis of Networked Control Systems over Unknown Channels