Robust stability of event-triggered nonlinear moving horizon estimation

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.

💡 Research Summary

This paper introduces an event‑triggered moving horizon estimator (ET‑MHE) designed for remote state estimation of general nonlinear discrete‑time systems. The key novelty lies in transmitting only a single measurement whenever an event is triggered, rather than a batch of past measurements, and solving the nonlinear MHE optimization problem only at those event times. When no event occurs, the estimator updates the state estimate by open‑loop propagation using the known system dynamics.

The authors first formalize the problem setting. The plant evolves as
x_{t+1}=f(x_t,u_t,w_t), y_t=h(x_t,u_t,w_t),
with bounded process disturbance and measurement noise w_t. A detectability assumption is imposed: the system must be exponentially incrementally input‑output‑to‑state stable (exponential i‑IOSS). This property guarantees the existence of a quadratic i‑IOSS Lyapunov function and is a necessary condition for robust exponential stability of any estimator.

The ET‑MHE algorithm is built around a binary triggering variable γ_t∈{0,1}. If γ_t=1, the current measurement y_{t‑1} is sent to the remote estimator, which then solves a nonlinear program (NLP) over a horizon of length M_t = min{t, M+δ_t}. Here δ_t denotes the number of steps since the last event, so the horizon automatically expands when communication is sparse. If γ_t=0, the estimator simply propagates the previous optimal state estimate forward (open‑loop prediction) without solving the NLP. The set K_s = {τ | γ_{τ+1}=1} collects all time indices whose measurements have actually been transmitted.

The cost function employed in the NLP consists of a prior term and a discounted stage cost:

J = η^{M_t}‖\hat{x}{t‑M_t}−\hat{x}{t‑M_t}‖{P_2}^2
 + Σ{j∈