State Estimation under Lebesgue Sampling and an Approach to Event-Triggered Control

Abstract

In a standard setup of conventional state estimation problems, the output signal of a dynamical system is sampled at every regular time interval. This paper addresses an estimation problem under event-triggered sampling: an irregular sampling rule in which the output signal is sampled only when a specified event occurs. In particular, this paper focuses on the Lebesgue sampling, which is a type of event-triggered sampling such that the output signal is sampled only when it crosses specific thresholds. In the proposed estimation method, not only information in the sampled points but also that in the inter-sample intervals are utilized to improve the estimation accuracy efficiently. The particle filter is applied to the estimation since the inter-sample information makes the distribution of the estimates non-Gaussian. Furthermore, the proposed estimator is combined with a linear-quadratic-regulator (LQR) type state-feedback controller. The derived control law can be an effective approach to an event-triggered control problem in which the Lebesgue-sampled output is utilized. The effectiveness of both of estimation and control methods is examined through numerical examples.