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Quadratic Invariance for Distributed Control System with Intermittent Observations

In this paper we consider a finite-horizon optimization problem with a distributed control policy. The local outputs are sent to a local controller in an intermittent fashion. As a consequence the controller has access to sensor information only if it is sent by the associated local scheduler or by neighboring controllers. We consider generalized event-triggered schedulers (which includes time-triggered schedulers as a special case, where time-instants define the events). This leads to an event-dependent information structure available at each local controller. As a result, the information structure changes, which potentially leads to a non-convex control design problem. For any event-triggered sensing topology, we give a necessary and sufficient condition for convexity of the optimal control problem, by using the quadratic invariance (QI) property. Furthermore, we provide an online algorithm that adapts the communication topology among the local controllers and guarantees a step-by-step QI, which translates to a global QI.