$$H_{\infty }$$ H ∞ Estimation for Markovian Jump Neural Networks With Quantization, Transmission Delay and Packet Dropout

Abstract

This paper is concerned with the problem of robust H ∞ estimation for a class of Markovian jump neural networks with norm-bounded parameter uncertainties, time-varying delay and limited communication capacity including signal transmission delay, measurement quantization and data packet dropout, which occur simultaneously in the same networked control system framework. Our objective is to design mode-dependent H ∞ filter in the network environment in order to ensure the filtering error system is not only exponentially mean-square stable, but also satisfies a prescribed H ∞ norm level for the limited communication capacity and for all admissible uncertainties. We use the delay system method to deal with signal transmission delay and data packet dropout, utilize the sector bound approach to handle measurement quantization. We also construct a comprehensive stochastic Lyapunov-Krasovskii functional to show the inherent mode-dependent state delays in the neural networks itself and the network-induced signal transmission delay. The free-weighting matrix technique and a set of strict linear matrix inequalities are employed to derive novel conditions for the desired mode-dependent H ∞ filter. A numerical example is provided to verify the effectiveness and usefulness of the obtained main results.

Event-triggered H∞ filtering for discrete-time Markov jump delayed neural networks with quantizations

“…Case 1: σ 1 = σ 2 and Case 2: σ 1 = σ 2 . For Case 1, the event-triggered parameter σ 1 = σ 2 = 0.2, when d m = 1, d M = 4, the maximum delay in communication network τ M = 5, and = 1, γ = 3, by using the LMI toolbox of Matlab, it is easy to obtain the following matrices: For Case 2, the event-triggered parameter σ 1 = 0.2, σ 2 = 0.1, when d m = 1, d M = 4, the maximum delay in communication network τ M = 5, and = 1, γ = 3, by using the LMI toolbox of Matlab, it is easy to obtain the following matrices: Remark IV.1: Although some feasible results have been developed in the existing literature to deal with H ∞ filter (estimation) for neural networks with quantizations (Sasirekha et al, 2017;Zhuang et al, 2016), they are difficult to be applied directly to deal with the case that exist in the event-triggered scheme. Comparing the existing literature and simulation results, we can easily conclude that the event-triggered mechanism can reduce the use of network bandwidth effectively.…”

“…In general, the neural networks display a characteristics of network modes jumps and such jumps are commonly considered to be determined by a time homogeneous Markov chain. With the aid of analysis and synthesis methodologies in the area of Markov jump linear systems (MJLSs) (Oliveira, Vargas, DoVal, & Peres, 2014;Xia, Sun, Teng, & Zhang, 2014), the resulting Markov jump neural networks (MJNNs) attract widely research interests, and a great number of literature are carried out for MJNNs, for more details, see Stoica and Yaesh (2008), Zhang, Zhu, Shi, and Zhao (2015), Zhuang, Ma, Xia, and Zhang (2016), Ren, Liu, Zhu, Zhong, and Shi (2017). Moreover, the filtering problems for neural networks are extensively studied by many researchers via various methodologies (Bao & Cao, 2011;Huang, Huang, & Chen, 2015).…”

“…The H ∞ state estimation problem for a class of discrete-time neural networks with timevarying delays, randomly occurring quantizations and missing measurements is addressed in Zhang, Wang, Ding, and Liu (2015). The problem of robust H ∞ estimation for a class of MJNNs with transmission delay, measurement quantization and data packet dropout is studied in Zhuang et al (2016). In Sasirekha, Rakkiyappan, Cao, Wan, and Alsaedi (2017), H ∞ state estimation of discrete-time Markov jump neural networks with general transition probabilities and output quantization is described.…”

Event‐triggered filter design for Markovian jump delay systems with nonlinear perturbation using quantized measurement

“…For instance, in the work of Shi et al, the design problem of sliding mode observer using quantized measurements was investigated for Markovian jump systems against actuator faults. The H ∞ filter was designed in the work of Zhuang et al for Markovian jump neural networks, where the limited communication capacity is assumed to contain signal transmission delay, measurement quantization, and data packet dropout. The quantized H ∞ filtering problem for a class of discrete‐time linear parameter‐varying systems with Markovian jumping parameters was studied in the work of Yao et al Very recently, the design problem of event‐triggered state estimator for Markovian jump systems with quantization and randomly occurring nonlinear perturbations was investigated in the work of Zha et al However, it is worth mentioning that the filter design problem for Markovian jump systems with both event‐triggered scheme and quantization is much complicated.…”

H∞ Control for Discrete-Time Networked T-S Fuzzy Systems with Packet Loss Based on Event-Triggered Mechanism

“…It is well known that packet loss often arises in the network transmission. To solve this problem, in [24], the data measurements processes from the plant to the filter are subject to random packet loss which satisfies Bernoulli distribution with bounded nonlinearity. In [25,26], the network-based output tracking control is investigated for a T-S fuzzy system and it is concluded that the system cannot be stabilized by a nondelayed fuzzy static output feedback controller but can be stabilized by a delayed fuzzy static output feedback controller.…”