Self-Triggered Output-Feedback Control of LTI Systems Subject to Disturbances and Noise

TL;DR

This paper develops a self-triggered control strategy for LTI systems with disturbances and noise, ensuring stability and efficient communication by estimating worst-case triggering times using ellipsoidal set-based methods.

Contribution

It introduces a novel STC approach that accounts for noise and disturbances, building on PETC stability results and employing set-based state estimation for practical implementation.

Findings

Additive noise does not prevent stability of output-feedback PETC.

The proposed STC predicts worst-case triggering times using ellipsoidal reachability.

The method is computationally tractable with some conservatism.

Abstract

Self-triggered control (STC) and periodic event-triggered control (PETC) are aperiodic sampling techniques aiming at reducing control data communication when compared to periodic sampling. In both techniques, the effects of measurement noise in continuous-time systems with output feedback are unaddressed. In this work we prove that additive noise does not hinder stability of output-feedback PETC of linear time-invariant (LTI) systems. Then we build an STC strategy that estimates PETC's worst-case triggering times. To accomplish this, we use set-based methods, more specifically ellipsoidal sets, which describe uncertainties on state, disturbances and noise. Ellipsoidal reachability is then used to predict worst-case triggering condition violations, ultimately determining the next communication time. The ellipsoidal state estimate is recursively updated using guaranteed state estimation (GSE) methods. The proposed STC is designed to be computationally tractable at the expense of some added conservatism. It is expected to be a practical STC implementation for a broad range of applications.