Event-triggered sampling control for stability and stabilization of memristive neural networks with communication delays
TL;DR: This paper investigates the global asymptotic stability and stabilization of memristive neural networks (MNNs) with communication delays via event-triggered sampling control through a newly augmented Lyapunov-Krasovskii functional.
About: This article is published in Applied Mathematics and Computation.The article was published on 2017-10-01. It has received 178 citations till now. The article focuses on the topics: Control theory & Exponential stability.
Citations
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TL;DR: A modified loose-looped fuzzy membership functions (FMFs) dependent Lyapunov-Krasovskii functional (LKF) is constructed based on the information of the time derivative of FMFs, which involves not only a signal transmission delay but also switched topologies.
246 citations
TL;DR: An adaptive event-triggered scheme for S-MJSs that is more effective than conventional event- triggered strategy for decreasing network transmission information is developed and a new adaptive law is designed that can dynamically adjust the event-Triggered threshold is designed.
Abstract: This paper examines the adaptive event-triggered fault detection problem of semi-Markovian jump systems (S-MJSs) with output quantization. First, we develop an adaptive event-triggered scheme for S-MJSs that is more effective than conventional event-triggered strategy for decreasing network transmission information. Meanwhile, we design a new adaptive law that can dynamically adjust the event-triggered threshold. Second, we consider output signal quantization and transmission delay in the proposed fault detection scheme. Moreover, we establish novel sufficient conditions for the stochastic stability in the proposed fault detection scheme with an $H_{\infty }$ performance with the help of linear matrix inequalities (LMIs). Finally, we provide simulation results to demonstrate the usefulness of the developed theoretical results.
183 citations
TL;DR: A novel stochastic switched sampled-data controller with time-varying sampling is developed in the frame of the zero-input strategy and novel synchronization criteria are established to guarantee that DCNNs are synchronous exponentially when the control packet dropout occurs in a random way.
125 citations
TL;DR: Four different kinds of feedback controllers are designed, under which the considered inertial memristor-based neural networks can realize fixed-time synchronization perfectly and the obtained fixed- time synchronization criteria can be verified by algebraic operations.
115 citations
TL;DR: This paper is concerned with the problem of synchronization for inertial neural networks (INNs) with heterogeneous time-varying delays (HTVDs) through quantized sampled-data control and a novel Lyapunov–Krasovskii functional is constructed for synchronizing an error system.
Abstract: This paper is concerned with the problem of synchronization for inertial neural networks (INNs) with heterogeneous time-varying delays (HTVDs) through quantized sampled-data control. The control scheme, which takes the communication limitations of quantization and variable sampling into account, is first employed for tackling the synchronization of INNs. A novel Lyapunov–Krasovskii functional (LKF) is constructed for synchronizing an error system. Compared with existing LKFs by the largest upper bound of all HTVDs, the proposed LKF is superior, since it can make full use of the information on the lower and upper bounds of each HTVD. Based on the LKF and a new integral inequality technique, less conservative synchronization criteria are derived. The desired quantized sampled-data controller is designed by solving a set of linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness and conservatism reduction of the proposed results.
94 citations
References
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TL;DR: It is shown, using a simple analytical example, that memristance arises naturally in nanoscale systems in which solid-state electronic and ionic transport are coupled under an external bias voltage.
Abstract: Anyone who ever took an electronics laboratory class will be familiar with the fundamental passive circuit elements: the resistor, the capacitor and the inductor. However, in 1971 Leon Chua reasoned from symmetry arguments that there should be a fourth fundamental element, which he called a memristor (short for memory resistor). Although he showed that such an element has many interesting and valuable circuit properties, until now no one has presented either a useful physical model or an example of a memristor. Here we show, using a simple analytical example, that memristance arises naturally in nanoscale systems in which solid-state electronic and ionic transport are coupled under an external bias voltage. These results serve as the foundation for understanding a wide range of hysteretic current-voltage behaviour observed in many nanoscale electronic devices that involve the motion of charged atomic or molecular species, in particular certain titanium dioxide cross-point switches.
8,971 citations
TL;DR: In this article, the memristor is introduced as the fourth basic circuit element and an electromagnetic field interpretation of this relationship in terms of a quasi-static expansion of Maxwell's equations is presented.
Abstract: A new two-terminal circuit element-called the memristorcharacterized by a relationship between the charge q(t)\equiv \int_{-\infty}^{t} i(\tau) d \tau and the flux-linkage \varphi(t)\equiv \int_{- \infty}^{t} v(\tau) d \tau is introduced as the fourth basic circuit element. An electromagnetic field interpretation of this relationship in terms of a quasi-static expansion of Maxwell's equations is presented. Many circuit-theoretic properties of memistors are derived. It is shown that this element exhibits some peculiar behavior different from that exhibited by resistors, inductors, or capacitors. These properties lead to a number of unique applications which cannot be realized with RLC networks alone. Although a physical memristor device without internal power supply has not yet been discovered, operational laboratory models have been built with the help of active circuits. Experimental results are presented to demonstrate the properties and potential applications of memristors.
7,585 citations
Book•
30 Sep 1988
TL;DR: The kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics, algebraic geometry interacts with physics, and such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes.
Abstract: Approach your problems from the right end It isn't that they can't see the solution It is and begin with the answers Then one day, that they can't see the problem perhaps you will find the final question G K Chesterton The Scandal of Father 'The Hermit Clad in Crane Feathers' in R Brown 'The point of a Pin' van Gulik's The Chinese Maze Murders Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes They draw upon widely different sections of mathematics
6,398 citations