An Event‐triggered Zonotopic Gaussian State Estimator for Discrete‐time Stochastic Multiplicative Systems with Zonotopic Set‐membership and Stochastic Uncertainties

SummaryThis article addresses the challenge of estimating the state of a discrete‐time stochastic multiplicative system with zonotopic set‐membership and stochastic uncertainties. The stochastic system model incorporates additive and multiplicative Gaussian and zonotopic set‐membership uncertainties, posing challenges in accurately managing these sources of uncertainty. In practical scenarios with limited communication resources, it is crucial to reduce communication overhead, save resources, and prevent unnecessary information transmission. To achieve these objectives, this article proposes an event‐triggered mechanism and a corresponding state estimator. The optimal gain matrix of the state estimator is derived to minimize the estimation uncertainty represented by the size of zonotope and Gaussian confidence ellipsoid regions. Conditions are established to guarantee the mean square stability of the estimation error, ensuring reliable estimation performance. The configuration of the triggering condition parameters, which play a vital role in determining the event‐triggered updates, is presented. is presented. The effectiveness of the proposed event‐triggered mechanism and the corresponding estimator is demonstrated through simulation results and analyses, using specific metrics and evaluation criteria.