Free-matrix-based time-dependent discontinuous Lyapunov functional for synchronization of delayed neural networks with sampled-data control

This paper is concerned with the synchronization of delayed neural networks via sampled-data control. A new technique, namely, the free-matrix-based time-dependent discontinuous Lyapunov functional approach, is adopted in constructing the Lyapunov functional, which takes advantage of the sampling characteristic of sawtooth input delay. Based on this discontinuous Lyapunov functional, some less conservative synchronization criteria are established to ensure that the slave system is synchronous with the master system. The desired sampled-data controller can be obtained through the use of the linear matrix inequality（LMI） technique. Finally, two numerical examples are provided to demonstrate the effectiveness and the improvements of the proposed methods.

On the functions of astrocyte-mediated neuronal slow inward currents

Slow inward currents are known as neuronal excitatory currents mediated by glutamate release and activation of neuronal extra synaptic N-met hyl-D-aspartate receptors with the contribution of astrocytes.These events are significantly slower than the excitatory postsynaptic currents.Parameters of slow inward currents are determined by seve ral factors including the mechanisms of astrocytic activation and glutamate release,as well as the diffusion pathways from the release site towards the extra synaptic recepto rs.Astrocytes are stimulated by neuronal network activity,which in turn excite neurons,forming an astrocyte-neuron feedback loop.Mostly as a consequence of brain edema,astrocytic swelling can also induce slow inward currents under pathological conditions.There is a growing body of evidence on the roles of slow inward currents on a single neuron or local network level.These events often occur in synchro ny on neurons located in the same astrocytic domain.Besides synchronization of neuronal excitability,slow inward currents also set synaptic strength via eliciting timing-dependent synaptic plasticity.In addition,slow inward currents are also subject to non-synaptic plasticity triggered by long-la sting stimulation of the excitatory inputs.Of note,there might be important regionspecific differences in the roles and actions triggering slow inward currents.In greater networks,the pathophysiological roles of slow inward currents can be better understood than physiological ones.Slow inward currents are identified in the pathophysiological background of autism,as slow inward currents drive early hypersynchrony of the neural networks.Slow inward currents are significant contributors to paroxysmal depolarizational shifts/interictal spikes.These events are related to epilepsy,but also found in Alzheimer's disease,Parkinson's disease,and stroke,leading to the decline of cognitive functions.Events with features overlapping with slow inward currents(excitatory,N-methyl-Daspartate-receptor mediated currents with astrocytic contribution) as ischemic currents and spreading depolarization also have a well-known pathophysiological role in worsening consequences of stroke,traumatic brain injury,or epilepsy.One might assume that slow inward currents occurring with low frequency under physiological conditions might contribute to synaptic plasticity and memory formation.However,to state this,more experimental evidence from greater neuronal networks or the level of the individual is needed.In this review,I aimed to summarize findings on slow inward currents and to speculate on the potential functions of it.

Synchronization criteria for multiple memristor-based neural networks with time delay and inertial term

This present work uses different methods to synchronize the inertial memristor systems with linear coupling. Firstly, the mathematical model of inertial memristor-based neural networks(IMNNs) with time delay is proposed, where the coupling matrix satisfies the diffusion condition, which can be symmetric or asymmetric. Secondly, by using differential inclusion method and Halanay inequality, some algebraic self-synchronization criteria are obtained. Then, via constructing effective Lyapunov functional, designing discontinuous control algorithms, some new sufficient conditions are gained to achieve synchronization of networks. Finally, two illustrative simulations are provided to show the validity of the obtained results, which cannot be contained by each other.

Adaptive Performance-Constrained Synchronization Control for Hypersonic Flight Vehicle Swarms: A Novel Finite-Time Convergence Protocol Methodology

This paper proposes a novel neural adaptive performance-constrained synchronization tracking control algorithm for multiple hypersonic flight vehicles(HFVs),which are subject to actuator faults and full-state constraints.The proposed method is based on advanced Lyapunov finite-time stability theory and a sophisticated backstepping design scheme.The longitudinal model of HFV is converted into velocity and altitude subsystems through functional decomposition.Our method presents three significant contributions over the existing state-of-the-art approaches:(a)ensuring finite-time convergence of HFVs systems by guaranteeing that the setting time is lower bounded by a positive constant that is related to the initial states;(b)utilizing a tan-type Barrier Lyapunov function(BLF)to ensure that the synchronization tracking errors of velocity,altitude,flight path angle,angle of attack,and pitch angle rate are maintained within certain performance bounds;and(c)designing a neural adaptive control algorithm and adaptive parameter laws by combining the backstepping design technique and radial basisfunction neural networks(RBFNNs)to handle unknown actuator faults and modeling uncer-tainties.Finally,comparative simulations are conducted to validate the efficacy of the proposed scheme.

Exponential stability of memristor-based synchronous switching neural networks with time delays

In this paper, we study the existence, uniqueness and stability of memristor-based syn- chronous switching neural networks with time delays. Several criteria of exponential stability are given by introducing multiple Lyapunov functions. In comparison with the existing publications on simplice memristive neural networks or switching neural net- works, we consider a system with a series of switchings, these switchings are assumed to be synchronous with memristive switching mechanism. Moreover, the proposed stability conditions are straightforward and convenient and can reflect the impact of time delay on the stability. Two examples are also presented to illustrate the effectiveness of the theoretical results.