Protocol-based state estimation for delayed Markovian jumping neural networks

Abstract

This paper is concerned with the state estimation problem for a class of Markovian jumping neural networks (MJNNs) with sensor nonlinearities, mode-dependent time delays and stochastic disturbances subject to the Round-Robin (RR) scheduling mechanism. The system parameters experience switches among finite modes according to a Markov chain. As an equal allocation scheme, the RR communication protocol is introduced for efficient usage of limited bandwidth and energy saving. The update matrix method is adopted to deal with the periodic time-delays resulting from the RR protocol. The objective of the addressed problem is to construct a state estimator for the MJNNs such that the dynamics of the estimation error is exponentially ultimately bounded in the mean square with a certain upper bound. Sufficient conditions are established for the existence of the desired state estimator by resorting to a combination of the Lyapunov stability theory and the stochastic analysis technique. Furthermore, the estimator gain matrices are characterized in terms of the solution to a convex optimization problem. Finally, a numerical simulation example is exploited to demonstrate the effectiveness of the proposed estimator design strategy.

$$H_\infty $$ State Estimation for Round-Robin Protocol-Based Markovian Jumping Neural Networks with Mixed Time Delays

“…Remark 3 Within the RRP scheduling, Theorem 1 makes a significant contribution to the asymptotical stability of estimation error dynamics that show the prescribed H ∞ performance, which is quite different from the existing results for the MJNNs on the exponential state estimation problem reported in [1,25]. Making use of a suitable Lyapunov-Krasovskii functional and the stochastic mathematical approaches, the asymptotical stability can be eventually demonstrated by finding a series of LMIs solutions, and implies that the stability criterion depends strongly on both the communication protocol and the Markovian switching signal.…”

“…In the last several years, artificial neural networks (ANNs) have been extensively applied in various fields, including automatic control, biology, and finance. In some practical applications such as pattern recognition and dynamical optimization, the analysis of ANNs dynamics have attracted increasing research interest [1][2][3][4][5][6]. Because of the limited conversion performance of amplifiers and inherent time for information transfer between neurons, time delay is inevitable and may cause some complex dynamical phenomena including oscillatory property, bifurcation, chaos and even instability.…”

On finite-horizon H∞ state estimation for discrete-time delayed memristive neural networks under stochastic communication protocol

“…To handle these network-induced challenges, an effective measure is to leverage communication protocols that help regulate the data transmission, and some widely deployed protocols include the event-triggering protocol (EEP), Round-Robin protocol (RRP), stochastic communication protocol (SCP) and try-once-discard protocol (TODP), see [41,42,5,44]. For example, the EEP has been successfully applied to the MNNs for the purpose of saving communication resources in [20,9], and the RRP and SCP have been applied to the traditional RNNs with the view of avoiding data collisions in [17,32]. Nevertheless, to our best knowledge, very few results have been acquired so far on the finite-time H ∞ SE problem for delayed MNNs, not to mention the case where the energy-bounded disturbances and SCP are both embraced.…”

Protocol‐based collaborative design for discrete‐time switched systems with sojourn probabilities

“…Therefore, some communication protocols are considered in networked controlled systems so as to improve the reliability of the data information and mitigate the communication burden. The representative protocols include the round‐Robin (RR) protocol, 27 the TOD protocol, 28‐30 the stochastic communication protocol, 31,32 and the event‐triggered protocol 33‐35 . To be specific, the TOD protocol is that only one sensor node could be granted the access right to transmit information according to certain prescribed principles.…”