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

Abstract

Self-triggered control (STC) is a sample-and-hold control method aimed at reducing communications in networkedcontrol systems; however, existing STC mechanisms often maximize how late the next sample is, thus not optimizing sampling performance in the long-term. In this work, we devise a method to construct self-triggered policies that provide nearmaximal average inter-sample time (AIST) while respecting given control performance constraints. To achieve this, we rely on finite-state abstractions of a reference event-triggered control, while also allowing earlier samples. These early triggers constitute controllable actions of the abstraction, for which an AIST-maximizing strategy can be obtained by solving a meanpayoff game. We provide optimality bounds, and how to further improve them through abstraction refinement techniques.

Computing the average inter-sample time of event-triggered control using quantitative automata

“…Finally, natural extensions of this line of work are ongoing, such as extending it to systems with disturbances, in particular stochastic noise [30], as well as the usage of abstractions for synthesis of sampling strategies that maximize the closed-loop SAIST [22]. Case 3: θ /π = p/q, where p, q ∈ N are co-prime.…”

“…The concept of SACE simulation and its related results have been recently expanded to non-autonomous WTSs in[22], where the objective was to design sampling strategies instead of evaluating them. This expansion is not needed for the scope of this paper 4.…”

A Simpler Alternative: Minimizing Transition Systems Modulo Alternating Simulation Equivalence

“…Since all systems have the same model, only one traffic abstraction is needed. We use the abstraction method in [32], where a parameter 𝑙 ∈ N is given to define the depth of the abstraction process: the higher 𝑙 is, the tighter the simulation relation is w.r.t. the original infinite system.…”