Stability analysis of event-triggered anytime control with multiple control laws

TL;DR

This paper introduces a new Markov jump system-based stability analysis for event-triggered anytime control algorithms, enabling analysis of more complex schemes with multiple control laws and stochastic conditions.

Contribution

It develops a general model and stability analysis for E-SAC using Markov jump systems, extending analytical capabilities to more sophisticated control schemes.

Findings

Recovered stability conditions for existing E-SAC algorithms.

Extended analysis to complex E-SAC schemes with multiple control laws.

Provided a systematic approach for stability analysis of stochastic event-triggered control.

Abstract

To deal with time-varying processor availability and lossy communication channels in embedded and networked control systems, one can employ an event-triggered sequence-based anytime control (E-SAC) algorithm. The main idea of E-SAC is, when computing resources and measurements are available, to compute a sequence of tentative control inputs and store them in a buffer for potential future use. State-dependent Random-time Drift (SRD) approach is often used to analyse and establish stability properties of such E-SAC algorithms. However, using SRD, the analysis quickly becomes combinatoric and hence difficult to extend to more sophisticated E-SAC. In this technical note, we develop a general model and a new stability analysis for E-SAC based on Markov jump systems. Using the new stability analysis, stochastic stability conditions of existing E-SAC are also recovered. In addition, the proposed technique systematically extends to a more sophisticated E-SAC scheme for which, until now, no analytical expression had been obtained.