Distributed Stability Certification and Control from Local Data

Abstract: Most data-driven analysis and control methods rely on centralized access to system measurements. In contrast, we consider a setting in which the measurements are distributed across multiple agents and raw data are not shared. Each agent has access only to locally held samples, possibly as little as a single measurement, and agents exchange only locally computed signals. Consequently, no individual agent possesses sufficient information to identify the entire system or synthesize a controller independently. To address this limitation, we develop distributed dynamical algorithms that enable the agents to collectively compute global system certificates from local data. Two problems are addressed. First, for stable linear time-invariant (LTI) systems, the agents compute a Lyapunov certificate by solving the Lyapunov equation in a fully distributed manner. Second, for general LTI systems, they compute the stabilizing solution of the algebraic Riccati equation and hence the optimal linear-quadratic regulator (LQR). An initially proposed scheme guarantees practical convergence, while a subsequent augmented PI-type algorithm achieves exact convergence to the desired solution. We further establish robustness of the resulting LQR controller to uncertainty and measurement noise. The approach is illustrated through distributed Lyapunov certification of a quadruple-tank process and distributed LQR design for helicopter dynamics.