Distributed Learning of Optimal Controls for Linear Systems

While classic controller design methods rely on a model of the underlying dynamics, data-driven methods allow to compute controllers leveraging solely a set of previously recorded input-output trajectories, with relatively mild assumptions. Assuming knowledge of the dynamics is especially unrealistic in decentralized systems, since information is typically localized by design. In this paper we investigate a decentralized data-driven approach to learn quadraticallyoptimal controls for interconnected linear systems. Our main result is a distributed algorithm that computes a control input to reach a desired target configuration with provable, and tunable, suboptimality guarantees. Our distributed procedure converges after a finite number of iterations and the suboptimality gap can be characterized analytically in terms of the data properties. Our algorithm relies on a new set of closed-form data-driven expressions of quadratically-optimal controls, which complement the existing literature on data-driven linear-quadratic control. We complement and validate our theoretical analysis by means of numerical simulations with different interconnected systems.