On the Robustness of Data-Driven Controllers for Linear Systems
This work addresses security and reliability concerns for control systems using data-driven methods, but it is incremental as it builds on existing frameworks with specific bounds.
The paper tackles the problem of quantifying the robustness of data-driven controllers for linear systems against adversarial data corruption, deriving probabilistic bounds on stability and convergence based on perturbation statistics and system properties.
This paper proposes a new framework and several results to quantify the performance of data-driven state-feedback controllers for linear systems against targeted perturbations of the training data. We focus on the case where subsets of the training data are randomly corrupted by an adversary, and derive lower and upper bounds for the stability of the closed-loop system with compromised controller as a function of the perturbation statistics, size of the training data, sensitivity of the data-driven algorithm to perturbation of the training data, and properties of the nominal closed-loop system. Our stability and convergence bounds are probabilistic in nature, and rely on a first-order approximation of the data-driven procedure that designs the state-feedback controller, which can be computed directly using the training data. We illustrate our findings via multiple numerical studies.