Decentralized LQ-Consistent Event-Triggered Control over a Shared Contention-Based Network

Consider a network of multiple independent stochastic linear systems where, for each system, a scheduler collocated with the sensors arbitrates data transmissions to a corresponding remote controller through a shared contention-based communication network. While the systems are physically independent, their optimal controller design problems may, in general, become coupled, due to network contention, if the schedulers trigger transmissions based on state-dependent events. In this article, we propose a class of probabilistic admissible schedulers for which the optimal controllers, with respect to local standard linear-quardatic Gaussian (LQG) costs, have the certainty equivalence property and can still be determined decentrally. Then, two subclasses of scheduling policies within this class are introduced; a nonevent-based subclass, so called purely stochastic transmission (PST) policy, and an event-based subclass, both with easily adjustable triggering probabilities at every time step. We then prove that, given a PST policy with given triggering probabilities and an associated closed-loop performance with optimal control law, we can find an event-based scheduler from the proposed subclass and with the same triggering probabilities for which the associated closed-loop performance with optimal control law is strictly superior. Moreover, we show that, for each closed-loop system, the optimal state estimators for both scheduling policies follows a linear iteration. Finally, we provide a method to regulate the triggering probabilities of the schedulers by maximizing a network utility function.