Hybrid impulsive and switching Hopfield neural networks with state-dependent impulses

Impulsive systems with growing numbers of chaotic attractors

Most classical chaotic systems, such as the Lorenz system and the Chua circuit, have chaotic attractors in bounded regions. This article constructs and analyzes a different kind of non-smooth impulsive systems, which have growing numbers of attractors in the sense that the number of attractors or the scrolls of an attractor is growing as time increases, and these attractors or scrolls are not located in bounded regions. It is found that infinitely many chaotic attractors can be generated in some of such systems. As an application, both theoretical and numerical analyses of an impulsive Lorenz-like system with infinitely many attractors are demonstrated.

Spiking Adaptive Dynamic Programming Based on Poisson Process for Discrete-Time Nonlinear Systems

In this article, a new iterative spiking adaptive dynamic programming (SADP) method based on the Poisson process is developed to solve optimal impulsive control problems. For a fixed time interval, combining the Poisson process and the maximum likelihood estimation (MLE), the three-tuple of state, spiking interval, and probability of Poisson distribution can be computed, and then, the iterative value functions and iterative control laws can be obtained. A property analysis method is developed to show that the value functions converge to optimal performance index function as the iterative index increases from zero to infinity. Finally, two simulation examples are given to verify the effectiveness of the developed algorithm.

IoT-Oriented Design of an Associative Memory Based on Impulsive Hopfield Neural Network with Rate Coding of LIF Oscillators

The smart devices in Internet of Things (IoT) need more effective data storage opportunities, as well as support for Artificial Intelligence (AI) methods such as neural networks (NNs). This study presents a design of new associative memory in the form of impulsive Hopfield network based on leaky integrated-and-fire (LIF) RC oscillators with frequency control and hybrid analog–digital coding. Two variants of the network schemes have been developed, where spiking frequencies of oscillators are controlled either by supply currents or by variable resistances. The principle of operation of impulsive networks based on these schemes is presented and the recognition dynamics using simple two-dimensional images in gray gradation as an example is analyzed. A fast digital recognition method is proposed that uses the thresholds of zero crossing of output voltages of neurons. The time scale of this method is compared with the execution time of some network algorithms on IoT devices for moderate data amounts. The proposed Hopfield algorithm uses rate coding to expand the capabilities of neuromorphic engineering, including the design of new hardware circuits of IoT.

Generalized norm for existence, uniqueness and stability of Hopfield neural networks with discrete and distributed delays

In this paper, the existence, uniqueness and stability criteria of solutions for Hopfield neural networks with discrete and distributed delays (DDD HNNs) are investigated by the definitions of three kinds of generalized norm (ξ-norm). A general DDD HNN model is firstly introduced, where the discrete delays τ_pq(t) are asynchronous time-varying delays. Then, {ξ,1}-norm, {ξ,2}-norm and {ξ,∞}-norm are successively used to derive the existence, uniqueness and stability criteria of solutions for the DDD HNNs. In the proof of theorems, special functions and assumptions are given to deal with discrete and distributed delays. Furthermore, a corollary is concluded for the existence and stability criteria of solutions. The methods given in this paper can also be used to study the synchronization and μ-stability of different DDD NNs. Finally, two numerical examples and their simulation figures are given to illustrate the effectiveness of these results.

Discrete Mutation Hopfield Neural Network in Propositional Satisfiability

The dynamic behaviours of an artificial neural network (ANN) system are strongly dependent on its network structure. Thus, the output of ANNs has long suffered from a lack of interpretability and variation. This has severely limited the practical usability of the logical rule in the ANN. The work presents an integrated representation of k-satisfiability (kSAT) in a mutation hopfield neural network (MHNN). Neuron states of the hopfield neural network converge to minimum energy, but the solution produced is confined to the limited number of solution spaces. The MHNN is incorporated with the global search capability of the estimation of distribution algorithms (EDAs), which typically explore various solution spaces. The main purpose is to estimate other possible neuron states that lead to global minimum energy through available output measurements. Furthermore, it is shown that the MHNN can retrieve various neuron states with the lowest minimum energy. Subsequent simulations performed on the MHNN reveal that the approach yields a result that surpasses the conventional hybrid HNN. Furthermore, this study provides a new paradigm in the field of neural networks by overcoming the overfitting issue.

Effects of infinite occurrence of hybrid impulses with quasi-synchronization of parameter mismatched neural networks

This article is deeply concerned with the effects of hybrid impulses on quasi-synchronization of neural networks with mixed time-varying delays and parameter mismatches. Hybrid impulses allow synchronizing as well as desynchronizing impulses in one impulsive sequence, so their infinite time occurrence with the system may destroy the synchronization process. Therefore, the effective hybrid impulsive controller has been designed to deal with the difficulties in achieving the quasi-synchronization under the effects of hybrid impulses, which occur all the time, but their density of occurrence gradually decrease. In addition, the new concepts of average impulsive interval and average impulsive gain have been applied to cope with the simultaneous existence of synchronizing and desynchronizing impulses. Based on the Lyapunov method together with the extended comparison principle and the formula of variation of parameters for mixed time-varying delayed impulsive system, the delay-dependent sufficient criteria of quasi-synchronization have been derived for two separate cases, viz., T_a<∞ and T_a=∞. Finally, the efficiency of the theoretical results has been illustrated by providing two numerical examples.

Effects of State-Dependent Impulses on Robust Exponential Stability of Quaternion-Valued Neural Networks Under Parametric Uncertainty

This paper addresses the state-dependent impulsive effects on robust exponential stability of quaternion-valued neural networks (QVNNs) with parametric uncertainties. In view of the noncommutativity of quaternion multiplication, we have to separate the concerned quaternion-valued models into four real-valued parts. Then, several assumptions ensuring every solution of the separated state-dependent impulsive neural networks intersects each of the discontinuous surface exactly once are proposed. In the meantime, by applying the B -equivalent method, the addressed state-dependent impulsive models are reduced to fixed-time ones, and the latter can be regarded as the comparative systems of the former. For the subsequent analysis, we proposed a novel norm inequality of block matrix, which can be utilized to analyze the same stability properties of the separated state-dependent impulsive models and the reduced ones efficaciously. Afterward, several sufficient conditions are well presented to guarantee the robust exponential stability of the origin of the considered models; it is worth mentioning that two cases of addressed models are analyzed concretely, that is, models with exponential stable continuous subsystems and destabilizing impulses, and models with unstable continuous subsystems and stabilizing impulses. In addition, an application case corresponding to the stability problem of models with unstable continuous subsystems and stabilizing impulses for state-dependent impulse control to robust exponential synchronization of QVNNs is considered summarily. Finally, some numerical examples are proffered to illustrate the effectiveness and correctness of the obtained results.

Asynchronous event-based sampling data for impulsive protocol on consensus of non-linear multi-agent systems

In this paper, we discuss the consensus problem of non-linear multi-agent systems where an impulsive protocol with event-based asynchronously sampled data is adopted. Systems that communicate by data asynchronously sampled in limited time intervals are constructed. By separating time instants at which the sampling and communication occur into different ones, resources for such activations that every agent must execute can be reallocated to reduce the system load at communication instants. Event-based schemes are introduced to manipulate the sampling behavior. Two cases that with and without leader in directed networks topologies are both investigated. Sufficient conditions for system parameters and the event-based sampling schemes are given to guarantee the consensus. Numerical simulations are presented to illustrate the effectiveness of our proposed method.

Exponential consensus of discrete-time non-linear multi-agent systems via relative state-dependent impulsive protocols

In this paper, we discuss the exponential consensus problem of discrete-time multi-agent systems with non-linear dynamics via relative state-dependent impulsive protocols. Impulsive protocols of which the impulsive instants are dependent on the weighted relative states of any two agents are introduced for general discrete-time multi-agent systems. The analysis of such impulsive protocols is transformed into an investigation on reduced fixed-time impulsive protocols by constructing a map, which is achieved mainly by a derived B-equivalence method in discrete-time domain. Our main results indicate that the exponential consensus of the multi-agent systems via relative state-dependent impulsive protocols can be achieved if the reduced systems via fixed-time impulsive protocols can achieve exponential consensus, which need to satisfy suitable sufficient conditions. Numerical simulations are presented to support the theoretical results.