Robust Event-Based Control: Bridge Time-Domain Triggering and Frequency-Domain Uncertainties

TL;DR

This paper analyzes the robustness of event-triggered control systems under frequency-domain uncertainties, revealing that sampling errors can be characterized as finite-gain stable operators, enabling robust controller design via standard $H_ty$ synthesis.

Contribution

It introduces a unified framework for analyzing and designing robust event-triggered controllers under various triggering mechanisms using IQC-based conditions.

Findings

Sampling errors are finite-gain $$ stable operators.

Robust control design reduces to standard $H_ty$ synthesis.

Algorithms for controller construction under different triggering schemes.

Abstract

This paper considers the robustness of event-triggered control of general linear systems against additive or multiplicative frequency-domain uncertainties. It is revealed that in static or dynamic event triggering mechanisms, the sampling errors are images of affine operators acting on the sampled outputs. Though not belonging to $\mathcal{RH}_\infty$, these operators are finite-gain $\mathcal{L}_2$ stable with operator-norm depending on the triggering conditions and the norm bound of the uncertainties. This characterization is further extended to the general integral quadratic constraint (IQC)-based triggering mechanism. As long as the triggering condition characterizes an $\mathcal{L}_2$-to-$\mathcal{L}_2$ mapping relationship (in other words, small-gain-type constraints) between the sampled outputs and the sampling errors, the robust event-triggered controller design problem can be transformed into the standard $H_\infty$ synthesis problem of a linear system having the same order as the controlled plant. Algorithms are provided to construct the robust controllers for the static, dynamic and IQC-based event triggering cases.