Optimal Control for LQG Systems on Graphs---Part I: Structural Results

In this two-part paper, we identify a broad class of decentralized output-feedback LQG systems for which the optimal control strategies have a simple intuitive estimation structure and can be computed efficiently. Roughly, we consider the class of systems for which the coupling of dynamics among subsystems and the inter-controller communication is characterized by the same directed graph. Furthermore, this graph is assumed to be a multitree, that is, its transitive reduction can have at most one directed path connecting each pair of nodes. In this first part, we derive sufficient statistics that may be used to aggregate each controller's growing available information. Each controller must estimate the states of the subsystems that it affects (its descendants) as well as the subsystems that it observes (its ancestors). The optimal control action for a controller is a linear function of the estimate it computes as well as the estimates computed by all of its ancestors. Moreover, these state estimates may be updated recursively, much like a Kalman filter

Direct data-driven control of linear time-varying systems

An identification-free control design strategy for discrete-time linear time-varying systems with unknown dynamics is introduced. The closed-loop system (under state feedback) is parametrised with data-dependent matrices obtained from an ensemble of input-state trajectories collected offline. Subsequently, controllers guaranteeing bounded closed-loop trajectories, optimal performance and robustness to process and measurement noise are designed via convex feasibility and optimisation problems involving purely data-dependent linear matrix inequalities. For the special case of periodically time-varying systems, performance guarantees are achieved over an infinite horizon, based on data collected over a single, finite duration experiment. The results are demonstrated by means of an illustrative academic example and a practically motivated example involving a voltage source converter.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl