To sample or not to sample: Self-triggered control for nonlinear systems

TL;DR

This paper introduces a self-triggered control approach for nonlinear systems that dynamically determines measurement and control update times based on the current state, reducing resource usage compared to traditional periodic control.

Contribution

It develops a novel self-triggered control method for nonlinear systems, specifically for state-dependent homogeneous and polynomial systems, avoiding periodic sampling.

Findings

Applicable to jet engine compressor and rigid body examples

Reduces resource usage compared to periodic control

Ensures stability and performance in nonlinear systems

Abstract

Feedback control laws have been traditionally implemented in a periodic fashion on digital hardware. Although periodicity simplifies the analysis of the mismatch between the control design and its digital implementation, it also leads to conservative usage of resources such as CPU utilization in the case of embedded control. We present a novel technique that abandons the periodicity assumption by using the current state of the plant to decide the next time instant in which the state should be measured, the control law computed, and the actuators updated. This technique, termed self-triggered control, is developed for two classes of nonlinear control systems, namely, state-dependent homogeneous systems and polynomial systems. The wide applicability of the proposed results is illustrated in two well known physical examples: a jet engine compressor and the rigid body.