Robust event-triggered state estimation: A risk-sensitive approach

In this work, we investigate a robust event-triggered remote state estimation problem for linear Gaussian systems with a stochastic event-triggering condition. The reference measure approach is used to obtain a robust event-triggered estimate that minimizes the so-called risk-sensitive criterion, which refers to the expectation of the exponential of the sum of the squared estimation error. We introduce the reference measure, under which, the measurements are identically independently distributed (i.i.d.) and independent of the states, and propose a map to link the “real-world” measure to the reference measure so that the recursions of the information states under the reference measure can be obtained. Based on these results, the risk-sensitive criteria are reformulated under the reference measure and closed-form expressions of the risk-sensitive event-triggered posterior and prior estimates are presented, which are shown to evolve in simple recursive Kalman-like structures. Moreover, two sufficient stability conditions for the proposed estimators are given, where the first requires the solution of a time-varying Riccati equation to be positive-definite and satisfy a specific inequality, which can be further extended to the scenario when the weighting matrix in the risk-sensitive criterion is time-variant; the second gives the range of values of the risk-sensitive parameter and covariance of the initial state for which the proposed estimators are stable. Comparative simulation results demonstrate that the proposed risk-sensitive event-triggered estimator is more robust to model uncertainties compared with a typical minimum mean squared error (MMSE) estimator with stochastic event-triggered sensor scheduling.