Robust stability of event-triggered nonlinear moving horizon estimation

TL;DR

The paper addresses robust remote state estimation for nonlinear systems under communication constraints by proposing an event-triggered moving horizon estimator (ET-MHE) that transmits a single measurement at each event and uses open-loop predictions between events. It proves robust global exponential stability (RGES) under an exponential i-IOSS detectability condition and demonstrates that a varying horizon length can tighten estimation error bounds. The approach reduces data transmission while maintaining strong stability guarantees, and it is validated through two nonlinear examples (batch reactor and robot arm) with analyses of triggering behavior and horizon-length effects. The results have practical implications for resource-constrained networked estimation in nonlinear settings and offer a foundation for extending to broader networked control applications.

Abstract

In this work, we propose an event-triggered moving horizon estimation (ET-MHE) scheme for the remote state estimation of general nonlinear systems. In the presented method, whenever an event is triggered, a single measurement is transmitted and the nonlinear MHE optimization problem is subsequently solved. If no event is triggered, the current state estimate is updated using an open-loop prediction based on the system dynamics. Moreover, we introduce a novel event-triggering rule under which we demonstrate robust global exponential stability of the ET-MHE scheme, assuming a suitable detectability condition is met. In addition, we show that with the adoption of a varying horizon length, a tighter bound on the estimation error can be achieved. Finally, we validate the effectiveness of the proposed method through two illustrative examples.

Figures (9)

• Figure 1: Diagram of the overall ET-MHE framework. The dashed arrows represent the communication that is only required in case of an event.
• Figure 2: Comparison of ET-MHE results for $\alpha=5$, MHE estimates (without event-triggering, i.e., $\alpha=0$) and real system states.
• Figure 3: Event scheduling variable $\gamma$ for simulation with $\alpha=5$.
• Figure 4: Average number of events for different choices of $\alpha$ for Example 1 (batch reactor), simulated over 60 time steps (i.e., 6 seconds).
• Figure 5: Two-link robot arm moving in a 2D-plane.

Theorems & Definitions (14)

• Definition 1: RGES Knu18
• Remark 1
• Remark 2
• Proposition 1: Kra24
• proof
• Remark 3
• Remark 4
• Theorem 1: RGES of ET-MHE
• proof
• Remark 5