Sample Complexity of Networked Control Systems Over Unknown Channels

Abstract

Recent control trends are increasingly relying on communication networks and wireless channels to close the loop for Internetof-Things applications. Traditionally these approaches are model-based, i.e., assuming a network or channel model they are focused on stability analysis and appropriate controller designs. However the availability of such wireless channel modeling is fundamentally challenging in practice as channels are typically unknown a priori and only available through data samples. In this work we aim to develop algorithms that rely on channel sample data to determine the stability and performance of networked control tasks. In this regard our work is the first to characterize the amount of channel modeling that is required to answer such a question. Specifically we examine how many channel data samples are required in order to answer with high confidence whether a given networked control system is stable or not. This analysis is based on the notion of sample complexity from the learning literature and is facilitated by concentration inequalities. Moreover we establish a direct relation between the sample complexity and the networked system stability margin, i.e., the underlying packet success rate of the channel and the spectral radius of the dynamics of the control system. This illustrates that it becomes impractical to verify stability under a large range of plant and channel configurations. We validate our theoretical results in numerical simulations.

Data-driven analysis and controller design for discrete-time systems under aperiodic sampling

“…Since the importance of data as well as of cyber-physical, embedded and networked control systems continues to grow, combining concepts from data-driven control and sampleddata control is a highly relevant research direction. The datadriven analysis of aperiodically sampled systems, as presented in this work, may contribute to this emerging field by providing a novel approach to model and analyze a great variety of problems at the intersection of data-driven and sampled-data control, such as learning event-triggered control [48], learning unknown channel conditions [49], or data-driven network access scheduling [50]. As in the continuous-time case, the crucial property of ∆ in the lifted domain is that it is static, i.e., the output e in each time interval N [t k ,t k+1 −1] depends on the input y in the same interval only.…”

Safe Learning-Based Control of Stochastic Jump Linear Systems: a Distributionally Robust Approach

“…which is of particular interest in networked control systems, it is shown in [26] that S for the closed-loop system with u(x) = Kx can be written explicitly as…”

Timer-Based Distributed Channel Access for Control Over Unknown Unreliable Time-Varying Communication Channels

“…In addition, it has been proven that boundedness of E{P k|k } guarantees that the feedback gain L ∞ is stabilizing due to the perfect communication link between the controller and actuators [3]. The certainty equivalence principle holds and consequently the control law ensures mean square boundedness of the state estimate and thus boundedness of the first term in (26). The first and last term of ( 26) are non-negative and bounded and thus the stability condition ( 23) only depends on the boundedness of E{P k|k }.…”

“…After proving the threshold-like structure of the optimal scheduling policy, iterative algorithms are designed to obtain the optimal solution without knowing the packet dropout rate. In a similar context, the relationship between the sample complexity and stability margin of a system over an unknown memoryless channel was investigated in [26]. Most recently, a multi-armed bandit (MAB) approach was proposed for near-optimal resource allocation [27].…”