State Estimation for Discrete-Time Neural Networks with Markov-Mode-Dependent Lower and Upper Bounds on the Distributed Delays

Abstract

This paper is concerned with the state estimation problem for a new class of discrete-time neural networks with Markovian jumping parameters and mixed time-delays. The parameters of the neural networks under consideration switch over time subject to a Markov chain. The networks involve both the discrete time-varying delay and the modedependent distributed time-delay characterized by the upper and lower boundaries dependent on the Markov chain. By constructing novel Lyapunov-Krasovskii functionals, sufficient conditions are firstly established to guarantee the exponential stability in mean square for the addressed discrete-time neural networks with Markovian jumping parameters and mixed time-delays. Then, the state estimation problem is coped with for the same neural network where the goal is to design a desired state estimator such that the estimation error approaches zero exponentially in mean square. The derived conditions for both the stability and the existence of desired estimators are expressed in the form of matrix inequalities that can be solved by the semi-definite programme method. A numerical simulation example is exploited to demonstrate the usefulness of the main results obtained.

Variance-constrained resilient $H_{\infty }$ state estimation for time-varying neural networks with randomly varying nonlinearities and missing measurements

“…where Λ 2 and Σ 2 are defined in (12), Λ 1 , Σ 1 , Γ 1 , Γ 2 , Γ 3 and Γ 4 are defined in (13). From the above inequalities, we can deduce that…”

“…Moreover, some useful state estimation algorithms have been given in [8] for delayed NNs to guarantee the H ∞ as well as passivity and in [9] for bidirectional associative NNs subject to mixed time-delays. During the analysis and implementation of the methods related to RNNs, it should be noticed that the neuron states may not always available in reality, so there is a need to estimate them by utilizing effective estimation methods [10][11][12]. Until now, many results have been published with respect to the state estimation problem of different types of dynamical networks [13][14][15][16].…”

State Estimation for Discrete-Time Stochastic Neural Networks with Mixed Delays

“…The condition on the activation function in Assumption 1 was originally employed in [27] and has been subsequently used in recent papers with the problem of stability of neural networks; see [5,6,11,28,29], for example.…”

“…As is known to all, many biological and artificial neural networks contain inherent time delays in signal transmission due to the finite speed of information processing, which may cause oscillation, divergence, and instability. In recent years, a great number of papers have been published on various networks with time delays [1][2][3][4][5][6][7][8][9][10].…”

Towards Robust Neural-Network-Based Sensor and Actuator Fault Diagnosis: Application to a Tunnel Furnace

“…In the case of non-linear dynamic system, the Artificial Neural Networks (ANNs) constitute an elegant remedy to the above-mentioned problem [4]. Unfortunately, the ANNs have disadvantages, e.g., they are usually not available in the state-space form [11,22,30] frequently used for fault diagnosis. Moreover, only rare approaches ensure the stability [21] and there is a limited number of solutions that can settle the robustness problems regarding neural model uncertainty [15,26].…”