Event-Triggered Control in Presence of Measurement Noise: A Space-Regularization Approach

Abstract

In this paper, general conditions for set stabilization of (distributed) event-triggered control systems affected by measurement noises are presented. It is shown that, under these conditions, both static and dynamic triggers can be designed using a space-regularization approach such that the closed-loop system ensures an input-to-state practical stability property. Additionally, by proper choice of the tuning parameters, the system does not exhibit Zeno behavior. Contrary to various results in the literature, the noises do not have to be differentiable. The general results are applied to point stabilization and consensus problems as particular cases. Simulations illustrate our results.

Event-Triggered State Estimation with Multiple Noisy Sensor Nodes

“…Moreover, when noises are present, we guarantee an inputto-state stability property of the estimation error dynamics, where we show that space-regularization (see [18]) can be used to obtain more favorable average inter-event times in the presence of non-vanishing noise. Numerical simulations illustrate the efficacy of our analysis and design framework.…”

“…Remark 2. As also noted in [18], selecting the constants s i such that s i > 0 will lead to practical stability. However, if the noise is non-vanishing, when the estimation error is close to 0, the inter-event times are generally close to τ i MIET , due to the trigger resets being 0 and ̺ i (the difference between the estimated state and the measured state) which are usually small.…”

“…Due to the trigger resets being (close to) 0, and the function ̺ i being generally small if the estimation error is close to the origin, the inter-event times are generally close to τ i MIET . When we add space-regularization, as in [18], the inter-event times are significantly larger. From Fig.…”

Output-Based Event-Holding Control in Presence of Measurement Noise

“…A famous example is the relative triggering mechanisms [9] for which Zeno behavior is excluded in the nominal case, but, it may occur when (arbitrary small) measurement noise is introduced, as shown in [10], [11]. To address this issue, in the previous works [7], [8], space-regularization was introduced, whereby the triggering condition is regularized using a tuning parameter. By selecting this tuning parameter sufficiently large, a MIET is guaranteed even in presence of noise, and the resulting stability property is an Input-to-State practical Stability (ISpS) property instead of an Input-to-State Stability (ISS) one.…”

Hybrid Systems with Continuous-time Inputs: Subtleties in Solution Concepts and Existence Results

“…Motivated by the gap in the literature regarding the study of existence and completeness properties of solutions to (1) given an input and the importance of this question in many application settings including hybrid control [9]- [12], networked control [13], [14] and event-triggered control [15]- [17] for plants subject to disturbances and/or measurement noise, we study in this paper the scenario where the input in ( 1) is fixed a priori and is a continuous-time measurable input defined on the nonnegative real line R 0 . Indeed, for these applications, it would be welcome to have such existence and completeness results, as they are often needed to guarantee that the designed controllers are well-posed in presence of external disturbance and noise signals.…”