Probabilistic‐constrained filtering for a class of nonlinear systems with improved static event‐triggered communication

This paper is concerned with the probabilistic‐constrained filtering problem for a class of time‐varying systems with stochastic nonlinearities and state constraints. An improved static event‐triggering scheme is used to reduce unnecessary signal transmissions on the communication channel, where a time‐varying triggering parameter is designed according to engineering practice. The aim of the problem addressed is to design a time‐varying filter such that (1) the prescribed probabilistic constraints on the estimation error are satisfied (ie, the probability for the estimation error to be confined to the given ellipsoidal set is larger than a prescribed value) and (2) the ellipsoid is minimized at each time instant in the sense of the matrix norm. First, the probabilistic constraints are handled by means of the multidimensional Chebyshev bounds. By using recursive matrix inequalities, stochastic analysis is conducted to establish sufficient conditions for the existence of the desired probabilistic‐constrained filter. Then, a recursive optimization algorithm is proposed to design the filter gain matrices. Finally, a simulation example is proposed to demonstrate the effectiveness and applicability of the proposed method.