On improved passivity criteria of uncertain neural networks with time-varying delays

In this paper, the problem of passivity analysis for uncertain neural networks with time-varying delays is considered. By constructing an augmented Lyapunov–Krasovskii’s functional and some novel analysis techniques, improved delay-dependent criteria for checking the passivity of the neural networks are established. The proposed criteria are represented in terms of LMIs (linear matrix inequalities) which can be easily solved by various convex optimization algorithms. Two numerical examples are included to show the superiority of our results.     

Passivity of uncertain neural networks with both leakage delay and time-varying delay

In this paper, the passivity problem is investigated for a class of uncertain neural networks with leakage delay and time-varying delay as well as generalized activation functions. By constructing appropriate Lyapunov–Krasovskii functionals, and employing Newton–Leibniz formulation and the free-weighting matrix method, several delay-dependent criteria for checking the passivity of the addressed neural networks are established in linear matrix inequality (LMI), which can be checked numerically using the effective LMI toolbox in MATLAB. Two examples with simulations are given to show the effectiveness and less conservatism of the proposed criteria.     

Passivity analysis of stochastic time-delay neural networks

Passivity analysis of stochastic neural networks with time-varying delays and parametric uncertainties is investigated in this paper. Passivity of stochastic neural networks is defined. Both delay-independent and delay-dependent stochastic passivity conditions are presented in terms of linear matrix inequalities (LMIs). The results are established by using the Lyapunov–Krasovskii functional method. In order to derive the delay-dependent passivity criterion, some free-weighting matrices are introduced. The effectiveness of the method is illustrated by numerical examples.     

State estimation of neural networks with time-varying delays and Markovian jumping parameter based on passivity theory

In this paper, the state estimation problem is investigated for neural networks with time-varying delays and Markovian jumping parameter based on passivity theory. The neural networks have a finite number of modes and the modes may jump from one to another according to a Markov chain. The main purpose is to estimate the neuron states, through available output measurements such that for all admissible time-delays, the dynamics of the estimation error is globally stable in the mean square and passive from the control input to the output error. Based on the new Lyapunov?CKrasovskii functional and passivity theory, delay-dependent conditions are obtained in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate effectiveness of the proposed method and results.     

Passivity analysis for discrete-time switched neural networks with various activation functions and mixed time delays

This paper is concerned with the passivity analysis for a class of discrete-time switched neural networks with various activation functions and mixed time delays. The mixed time delays under consideration include time-varying discrete delay and bounded distributed delay. By using the average dwell time approach and the discontinuous piecewise Lyapunov function technique, a novel delay-dependent sufficient condition for exponential stability of the switched neural networks with passivity is derived in terms of a set of linear matrix inequalities (LMIs). The obtained condition is not only dependent on the discrete delay bound, but also dependent on the distributed delay bound. A numerical example is given to demonstrate the effectiveness of the proposed result.     

New passivity criterion for limit cycle oscillation removal of interfered 2D digital filters in the Roesser form with saturation nonlinearity

The passivity concept plays an important role in circuit theory, signal processing, and control, but no criteria have yet been established for two-dimensional (2D) digital filters. In this article, we propose a new and first criterion for 2D digital filters in the Roesser form, to ensure passivity from the interference vector to the output vector with a certain storage function. The proposed criterion also guarantees the asymptotic stability of 2D digital filters in the Roesser form without interference. This criterion is described by linear matrix inequality, making it computationally attractive. A simulation example is presented, which demonstrates the usefulness of the 2D passivity criterion.     

Passivity analysis of delayed neural networks with discontinuous activations via differential inclusions

Without assuming the boundedness and monotonicity of neuron activations, we investigate passivity of delayed neural networks with discontinuous activations. Based on differential inclusion theory, sufficient conditions are established in form of linear matrix inequality by employing the generalized Lyapunov approach. In addition, a kind of control input is designed to stabilize neural network with activation functions having special form. Finally, some numerical examples are proposed to show the effectiveness of developed results.     

Switched exponential state estimation of neural networks based on passivity theory

In this paper, a new exponential state estimation method is proposed for switched Hopfield neural networks based on passivity theory. Through available output measurements, the main purpose is to estimate the neuron states such that the estimation error system is exponentially stable and passive from the control input to the output error. Based on augmented Lyapunov–Krasovskii functional, Jensen’s inequality, and linear matrix inequality (LMI), a new delay-dependent state estimator for switched Hopfield neural networks can be achieved by solving LMIs, which can be easily facilitated by using some standard numerical packages. The unknown gain matrix is determined by solving delay-dependent LMIs. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.     

Dissipativity of a class of cellular neural networks with proportional delays

In this paper, the problem of dissipativity is investigated for cellular neural networks with proportional delays. Without assuming monotonicity, differentiability, and boundedness of activation functions, two new delay-independent criteria for checking the dissipativity of the addressed neural networks are established by using inner product properties and matrix theory. Two examples and their simulation results are given to show the effectiveness and less conservatism of the proposed criteria.     

New augmented Lyapunov–Krasovskii functional approach to stability analysis of neural networks with time-varying delays

This paper is concerned with the problem of stability analysis for neural networks with time-varying delays. By constructing a newly augmented Lyapunov functional and some novel techniques, delay-dependent criteria to guarantee the asymptotic stability of the concerned networks are derived in terms of linear matrix inequalities (LMIs). The improvement of feasible region of the proposed criteria comparing with the previous works is shown by two numerical examples.     

Exponential stability in the mean square for stochastic neural networks with mixed time-delays and Markovian jumping parameters

In this paper, the stability analysis problem is considered for a class of stochastic neural networks with mixed time-delays and Markovian jumping parameters. The mixed delays include discrete and distributed time-delays, and the jumping parameters are generated from a continuous-time discrete-state homogeneous Markov process. The aim of this paper is to establish some criteria under which the delayed stochastic neural networks are exponentially stable in the mean square. By constructing suitable Lyapunov functionals, several stability conditions are derived on the basis of inequality techniques and the stochastic analysis. An example is also provided in the end of this paper to demonstrate the usefulness of the proposed criteria.     

Exponential synchronization of chaotic neural networks: a matrix measure approach

Based on matrix measure and Halanay inequality, exponential synchronization of a class of chaotic neural networks with time-varying delays is investigated. Without constructing Lyapunov function, some simple but generic criteria for exponential synchronization of chaotic neural networks are derived. It is shown that the obtained results are easy to verify and simple to implement in practice. Two examples are given to illustrate the effectiveness of the presented synchronization scheme.     

Global Attractivity and Global Exponential Stability for Delayed Hopfield Neural Network Models

ＩｎｔｒｏｄｕｃｔｉｏｎＨｏｐｆｉｅｌｄｎｅｕｒａｌｎｅｔｗｏｒｋｍｏｄｅｌｉｓｏｎｅｏｆｔｈｅｍｏｓｔｐｏｐｕｌａｒｍｏｄｅｌｓｉｎｔｈｅｌｉｔｅｒｒａｔｕｒｅｏｆａｒｔｉｆｉｃｉａｌｎｅｕｒａｌｎｅｔｗｏｒｋｓ,ｗｈｉｃｈｉｓｄｅｓｃｒｉｂｅｄｂｙｔｈｅｆｏｌｌｏｗｉｎｇｎｏｎｌｉｎｅａｒｄｙｎａｍｉｃｓｅｑｕａｔｉｏｎｓ[1,2 ]:Ｃｉｄｕｉ(ｔ)ｄｔ =-ｕｉ(ｔ)Ｒｉ ∑ｎｊ=1Ｔｉｊｇｊ(ｕｊ(ｔ) ) Ｉｉ　　 (ｉ=1 ,2 ,… ,ｎ) ,( 1 )ｗｈｅｒｅｎ≥ 2ｉｓｔｈｅｎｕｍｂｅｒｏｆｎｅｕｒｏｎｓｉｎｔｈｅ…     

Synchronization analysis of directed complex networks with time-delayed dynamical nodes and impulsive effects

In this paper, the effect of impulses on the synchronization of a class of general delayed dynamical networks is analyzed. The network topology is assumed to be directed and weakly connected with a spanning tree. Two types of impulses occurred in the states of nodes are considered: (i) synchronizing impulses meaning that they can enhance the synchronization of dynamical networks; and (ii) desynchronizing impulses defined as the impulsive effects can suppress the synchronization of dynamical networks. For each type of impulses, some novel and less conservative globally exponential synchronization criteria are derived by using the concept of average impulsive interval and the comparison principle. It is shown that the derived criteria are closely related with impulse strengths, average impulsive interval, and topology structure of the networks. The obtained results not only can provide an effective impulsive control strategy to synchronize an arbitrary given delayed dynamical network even if the original network may be asynchronous itself but also indicate that under which impulsive perturbations globally exponential synchronization of the underlying delayed dynamical networks can be preserved. Numerical simulations are finally given to demonstrate the effectiveness of the theoretical results.     

Projective and lag synchronization between general complex networks via impulsive control

This paper mainly investigates the projective and lag synchronization between general complex networks via impulsive control. A general drive complex network and an impulsively controlled slave network are presented in the model. Specially, the coupling matrix in this model is not assumed to be symmetric, diffusive or irreducible. Some criteria and corollaries are, respectively, derived for the projective synchronization and lag synchronization between the presented impulsively controlled complex networks. Finally, the results are illustrated by complex networks composed of the chaotic Lorenz systems. All the numerical simulations verify the correctness of the theoretical results.     

空间机器人捕获航天器后基于无源性理论的鲁棒镇定控制

研究了漂浮基空间机器人捕获非合作航天器过程对系统产生的冲击效应及其后联合体系统镇定运动的控制问题。为此,利用拉格朗日方法及牛顿-欧拉法分别获得了捕获前空间机器人及目标航天器的动力学模型;结合动量守恒定律、系统运动几何关系及力的传递规律,分析了捕获过程相互碰撞所产生的冲击效应,建立了捕获完成后两者联合体的系统动力学模型。在此基础上,针对同时存在不确定参数及外部扰动的联合体系统,设计了基于无源性理论的镇定运动神经网络H_∞鲁棒控制算法。本文提出的基于无源性理论设计的鲁棒控制算法具有良好的动态特性及较强的鲁棒性,可快速完成系统的镇定控制,实现轨迹的精确跟踪。系统数值模拟仿真验证了本文控制方案的正确性。     

Construction of hybrid 1D-0D networks for efficient and accurate blood flow simulations

The one-dimensional (1D) modeling of blood flow in complex networks of vessels and cardiovascular models can result in computationally expensive simulations. The complexity of such networks has significantly increased in the last years, in terms of both enhanced anatomical detail and modeling of physiological mechanisms and mechanical characteristics. To address such issue, the main goal of this work is to present a novel methodology to construct hybrid networks of coupled 1D and 0D vessels and to perform computationally efficient and accurate blood flow simulations in such networks. Departing from both the 1D and lumped-parameter (0D) nonlinear models for blood flow, we propose high-order numerical coupling strategies to solve the 1D, 0D, and hybrid coupling of vessels at junctions. To effectively construct hybrid networks, we explore different a-priori model selection criteria focusing in obtaining the best possible trade-off between computational cost of the simulations and accuracy of the computed solutions for the hybrid network with respect to the 1D network. The achievement of the expected order of accuracy is verified in several test cases. The novel methodology is applied to two different arterial networks, the 37-artery network and the reduced ADAN56 model, where, in order to identify the best performing a-priori model selection criteria, the quantitative assessment of CPU times and errors and the qualitative comparison between results are carried out and discussed.     

Mixed outer synchronization of dynamical networks with nonidentical nodes and output coupling

Outer synchronization between the drive network and the response network has attracted much more attention in various fields of science and engineering. In this paper, mixed outer synchronization between two complex dynamical networks with nonidentical nodes and output coupling is investigated via impulsive hybrid control, that is, an adaptive feedback controller with impulsive control effects. Moreover, both the cases of complex networks without and with coupling delay are considered. According to the stability analysis of the impulsive functional differential equation, several sufficient conditions for the networks to achieve mixed outer synchronization are derived. Numerical examples are presented finally to illustrate the effectiveness and advantage of the proposed synchronization criteria.     

Exponential synchronization of stochastic delayed discrete-time complex networks

This paper is concerned with the problem of synchronization for stochastic discrete-time drive-response networks with time-varying delay. By employing the Lyapunov functional method combined with the stochastic analysis as well as the feedback control technique, several sufficient conditions are established that guarantee the exponentially mean-square synchronization of two identical delayed networks with stochastic disturbances. These sufficient conditions, which are expressed in terms of linear matrix inequalities (LMIs), can be solved efficiently by the LMI toolbox in Matlab. A particular feature of the LMI-based synchronization criteria is that they are dependent not only on the connection matrices in the drive networks and the feedback gains in the response networks, but also on the lower and upper bounds of the time-varying delay, and are therefore less conservative than the delay-independent ones. Two numerical examples are exploited to demonstrate the feasibility and applicability of the proposed synchronization approaches.     

Pinning adaptive synchronization of complex dynamical network with multi-links

Networks with multi-links are universal in the real world such as communication networks, transport networks, and social networks. It is important for us to investigate the control of complex dynamical network with multi-links. In this paper, both local and global stabilities of dynamical network with multi-links are analyzed by applying adaptive control theory and mathematical tools, and some new criteria are proposed to ensure the pinning synchronization. We find that the number of pinned nodes satisfies an inequality for synchronization. Additionally, we solve the problem of how much the coupling strength we need to achieve network synchronization with one pinned node in the network system with multi-links. Finally, numerical examples are used to illustrate the effectiveness of the proposed method.