Some remarks on practical stabilization via CLF-based control under measurement noise

TL;DR

This paper presents a method for practical stabilization of input-affine systems with measurement noise using Lyapunov functions, self-triggered measurements, and control constraints, ensuring convergence to a target region.

Contribution

It introduces a systematic way to compute measurement accuracy and timing for stabilization under measurement noise and input constraints using Lyapunov-based decay conditions.

Findings

System converges into a target ball around the origin.

Measurement timing is optimized based on system dynamics.

Approach guarantees admissible control law under measurement errors.

Abstract

Practical stabilization of input-affine systems in the presence of measurement errors and input constraints is considered in this brief note. Assuming that a Lyapunov function and a stabilizing control exist for an input-affine system, the required measurement accuracy at each point of the state space is computed. This is done via the Lyapunov function-based decay condition, which describes along with the input constraints a set of admissible controls. Afterwards, the measurement time points are computed based on the system dynamics. It is shown that between these self-triggered measurement time points, the system evolves and converges into the so-called target ball, i.e. a vicinity of the origin, where it remains. Furthermore, it is shown that the approach ensures the existence of a control law, which is admissible for all possible states and it introduces a connection between measurement time points, measurement accuracy, target ball, and decay. The results of the approach are shown in three examples.