Asynchronous State Estimation for Markov Jump Neural Networks Under Complex Transition Probabilities: A Dynamic Event-Based Weighted Try-Once-Discard Protocol

This work focuses on the state estimation for hidden markov jump neural networks (MJNNs) under complex transition probabilities (C-TPs) and network-induced communication constraints. Obtaining precise transition probabilities (TPs) of a markov process is often challenging in practical scenarios. Therefore, this work considers the TPs may be unknown or imprecise, leading to the C-TPs situations, which are more practical for MJNNs. In order to save network resources and reduce data conflicts, a novel dynamic event-based weighted try-once-discard (DEWTOD) protocol is introduced. Unlike existing protocols, the DEWTOD protocol simultaneously determines the sampling instant and the node responsible for transmission. To accurately reflect the asynchronous phenomenon between the system and the estimator, this paper proposes a nonhomogeneous hidden Markov model, which the detection transition matrix is time-dependent and is characterized by a collection of polyhedra. Through a polytopic-structured Lyapunov function, some sufficient conditions are established to ensure mean-square exponential stability of the augmented systems. To this end, two examples are presented to demonstrate the effectiveness of the proposed estimator design method.