Quantized passive filtering for switched delayed neural networks

Abstract

The issue of quantized passive filtering for switched delayed neural networks with noise interference is studied in this paper. Both arbitrary and semi-Markov switching rules are taken into account. By choosing Lyapunov functionals and applying several inequality techniques, sufficient conditions are proposed to ensure the filter error system to be not only exponentially stable, but also exponentially passive from the noise interference to the output error. The gain matrix for the proposed quantized passive filter is able to be determined through the feasible solution of linear matrix inequalities, which are computationally tractable with the help of some popular convex optimization tools. Finally, two numerical examples are given to illustrate the usefulness of the quantized passive filter design methods.

Input‐to‐state learning of recurrent neural networks with delay and disturbance

“…According to the connectionism, NNs are mainly divided into feed‐forward NNs and recurrent NNs (RNNs), where RNNs are an extension of the traditional feed‐forward NNs and can successfully surmount the defects of the feed‐forward NNs 1 . Over the past several decades, many different models of RNNs covering Hopfield NNs, 2 Cohen–Grossberg competitive NNs, 3 fractional‐order NNs, 4 complex‐valued NNs, 5 reaction‐diffusion NNs, 6 memristive NNs, 7 and switched NNs, 8 have been discussed in the literature and their applications have been made in a multitude of areas, such as manipulator control, 9 secure communication, 10 image processing, 11 clinical medicine, 12 and so forth. It has been shown that the abundant dynamic behaviors of RNNs play a vital role in some of these applications.…”

Event‐triggered quantized L2−L∞$$ {\mathfrak{L}}_2-{\mathfrak{L}}_{\infty } $$ filtering for neural networks under denial‐of‐service attacks

“…A quantizer $$$ \Phi \left(\cdotp \right):{\mathbb{R}}^m\to {U}^m $$$ is given $$$ \Phi \left(\nu \right)={\left[{\Phi}_1\left({\nu}_1\right),\dots, {\Phi}_m\left({\nu}_m\right)\right]}^T $$$, where $$$ U=\left\{\pm {u}_j,{u}_j={\chi}^j{u}_0,j=0,\pm 1,\pm 2,\dots \right\}\cup \left\{0\right\} $$$ with $$$ {u}_0>0 $$$ and $$$ 0<\chi <1 $$$ 12,49,50 . For any $$$ {\nu}_a\in $$$ $$$ \mathbb{R}\left(a=1,\dots, m\right) $$$, the logarithmic quantizer $$$ {\Phi}_a\left({\nu}_a\right) $$$ is given by …”

“…, where U = {±u j , u j = 𝜒 j u 0 , j = 0, ±1, ±2, … } ∪ {0} with u 0 > 0 and 0 < 𝜒 < 1. 12,49,50 For any 𝜈 a ∈ R(a = 1, … , m), the logarithmic quantizer Φ a (𝜈 a ) is given by…”

“…Thereupon, it is particularly significant to estimate the neuron states by the available network measurements. Over the last decade, the filtering issue concerning NNs has long been a focus of attention and a great number of valid methods have been proposed; see, for instance, memory filtering, 6 command filtering, 7,8 $$$ {\mathscr{H}}_{\infty } $$$ filtering, 9,10 passive filtering, 11,12 and $$$ {\mathfrak{L}}_2-{\mathfrak{L}}_{\infty } $$$ filtering 13,14 . To be more specific, it was shown in Reference 9 that the reliable exponential $$$ {\mathscr{H}}_{\infty } $$$ filtering issue for switched reaction‐diffusion NNs was investigated, and a Luenberger observer was designed to ensure the error system with a exponential $$$ {\mathscr{H}}_{\infty } $$$ disturbance‐attenuation level.…”

Event-triggered dynamic output quantized control for 2-D switched systems

“…However, few authors focus on the output feedback control for 2-D systems, let alone 2-D switched systems. In recent years, based on the quantization technique, which is another effective method to save network bandwidth sources [15,29,34], the authors in [17] proposed an output quantized control for 2-D discrete switched complex networks.…”