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.

Abstracting the Sampling Behaviour of Stochastic Linear Periodic Event-Triggered Control Systems

“…Event-Triggered Control (ETC), has been thoroughly studied in the past two decades [1][2][3][4][5][6][7][8][9][10][11][12]. The vast majority of ETC research (e.g.…”

“…A different approach is based on abstractions [10][11][12], where a given ETC system is abstracted by a finite-state transition system. The set of the abstraction's output sequences contains all sampling patterns that can be exhibited by the ETC system.…”

“…But more importantly, the existing algorithms for computations over finite transition systems enable tractable ways of predicting sampling patterns and computing performance metrics. For instance, as argued in [10] and [11], such abstractions can be used for scheduling traffic in networks of ETC loops, while, in [12], abstractions were used to compute the minimum average interevent time of PETC systems.…”

“…So far, such abstractions have been developed only for non-stochastic systems: [10] and [12] considered LTI ETC systems, whereas [11] addressed nonlinear systems with bounded disturbances. However, for perturbed systems, the abstractions were conservative, due to the worst-case scenario approach that was followed.…”

“…It is the first one to abstract stochastic ETC sampling. Compared to [10][11][12], it uses a completely different abstraction framework (IMCs), owing to the need for different mathematical tools to analyze stochastic systems. The probabilities of going from one region to another with the interevent time obtaining a specific value, which can be thought of as reachability analysis for stochastic PETC systems, are investigated here for the first time.…”