Distributed control of systems with uncertain initial conditions

Abstract

This paper focuses on the control of distributed systems with uncertain initial conditions, where the constituent subsystems are interconnected over directed graphs and represented by discrete-time, linear time-varying models. Specifically, we consider distributed systems where the individual subsystems are eventually time-periodic, by which we mean that the state-space matrices of the subsystems are aperiodic for an initial amount of time and then become time-periodic afterwards. The information transfer between the subsystems is subjected to a delay of one sampling period. Independent norm constraints are placed on the disturbance input and the uncertain initial state. We present convex synthesis conditions for control design in this setting, employing a square l 2 induced norm as the performance measure. The synthesis conditions become finite-dimensional when the underlying graph has a finite set of vertices. An illustrative example on formation control of fixed-wing unmanned aircraft systems (UAS) is also provided.