Computing the sampling performance of event-triggered control

Abstract

In the context of networked control systems, event-triggered control (ETC) has emerged as a major topic due to its alleged resource usage reduction capabilities. However, this is mainly supported by numerical simulations, and very little is formally known about the traffic generated by ETC. This work devises a method to estimate, and in some cases to determine exactly, the minimum average intersample time (MAIST) generated by periodic event-triggered control (PETC) of linear systems. The method involves abstracting the traffic model using a bisimulation refinement algorithm and finding the cycle of minimum average length in the graph associated to it. This always gives a lower bound to the actual MAIST. Moreover, if this cycle turns out to be related to a periodic solution of the closed-loop PETC system, the performance metric is exact.

Self-Triggered Control for Near-Maximal Average Inter-Sample Time

“…To solve Problem 2, we adapt the abstraction framework of [12] to include quantitative capabilities; that is, we abstract our system as a weighted automaton, in a similar way as we did in [11].…”

“…These characteristics simplify the job of find an abstraction that is alternatingly weight simulated by S. We can do a standard quotient system [12] as in [15], where the motivation was to allow early triggers for scheduling of multiple control loops in a single shared network. Better than that, we can start from the lcomplete models [22] from [11], which can predict the next l deadlines if the PETC triggering strategy is used, and further augment the abstraction with early trigger actions. Hence, let us recover the relation in [11] that allows the construction of the quotient state-space: Definition 4 (Deadline sequence relation [11]): Given a sequence length l, we denote by R l ⊆ X × Y l the relation satisfying…”

“…Better than that, we can start from the lcomplete models [22] from [11], which can predict the next l deadlines if the PETC triggering strategy is used, and further augment the abstraction with early trigger actions. Hence, let us recover the relation in [11] that allows the construction of the quotient state-space: Definition 4 (Deadline sequence relation [11]): Given a sequence length l, we denote by R l ⊆ X × Y l the relation satisfying…”

“…Therefore, we choose to focus on the more practical Lyapunov-based ETC and STC strategies, even though their simplicity comes with a cost: the emerging traffic patterns are often erratic. In fact, even rigorously measuring the AIST of a given ETC implementation is challenging, and only recently a computational method to do this for periodic ETC (PETC, [10]) 1 has been proposed in [11].…”

“…This is attained by considering predicted PETC triggering times as deadlines: sampling earlier than these deadlines always ensures equal or better control performance, and done in the right way it can provide long-term benefits in terms of AIST. To determine when these long-term rewards are attained, we build on our recent work in [11] by using finite-state abstractions [12] of the reference PETC, and appending weights on the transitions systems, obtaining weighted automata [13]. Finitestate abstractions can simulate all possible behaviors of the concrete systems, while permitting computations that are otherwise intractable or impossible in infinite-state systems.…”