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This paper deals with the problem for synchronization of a nonlinear time delayed complex spatio-temporal network (CSN), modelled by semi-linear parabolic partial differential-difference equations. A boundary controller relying to distributed measurement is designed. Multiple time-invariant delays are firstly considered. By employing Lyapunov’s direct method and Wirtingers inequality, synchronization criteria of the CSN are presented in terms of LMIs. And then, multiple time-varying delays are respectively considered using the boundary controller and synchronization criteria are obtained. Finally, an example illustrates the effectiveness of the proposed method.

This paper investigates the synchronization problem for the realization-dependent probabilistic Boolean networks (PBNs) coupled unidirectionally in the drive-response configuration. The realization of the response PBN is assumed to be uniquely determined by the realization signal generated by the drive PBN at each discrete time instant. First, the drive-response PBNs are expressed in their algebraic forms based on the semitensor product method, and then, a necessary and sufficient condition is presented for the synchronization of the PBNs. Second, by resorting to a newly defined matrix operator, the reachable set from any initial state is expressed by a column vector. Consequently, an easily computable algebraic criterion is derived assuring the synchronization of the drive-response PBNs. Finally, three illustrative examples are employed to demonstrate the applicability and usefulness of the developed theoretical results.

By considering network transmission mode, this paper addresses the finite-time multi-switching synchronization problem for two kinds of multiple chaotic systems. For multiple same-order chaotic systems, we construct the general switching rules and analyze the existence of switching cases. The presented schemes guarantee the states of each derive system to be finite-timely synchronized with the desired states of every respond system in the different transmission paths and switching sequences. For multiple different order chaotic systems, we analyze a special multi-switching hybrid synchronization behavior, where part of the states are completely synchronized and the others belong to combination synchronization. Moveover, the easily verifiable criterion is derived for such synchronization. Finally, numerical examples are given to show the effectiveness of the presented theoretical results.

The study, by using aperiodically intermittent pinning control, is to synchronize switched delayed complex networks with unstable subsystems. Matrix $$\omega $$ -measure and mode-dependent average dwell time method are used to achieve globally exponential synchronization for such system. By designing the useful switching rule and control scheme, we obtain the novel synchronization criteria, which improve the conventional results. Finally, simulation analysis demonstrates the advantages of proposed innovations.

Two kinds of finite-time complex function synchronization for multiple complex-variable chaotic systems are investigated. Both the transmission mode and combination mode are respectively considered. By considering complex functions as the scaling factors, the definitions of the two different synchronization mechanisms are established, and the appropriate schemes are proposed to guarantee the finite-time stability of all error systems. Furthermore, two verifiable criteria are derived to synchronize multi-systems. Finally, detailed simulation analysis is provided to validate the effectiveness of all innovations.

This paper mainly investigates two kinds of sliding mode synchronization (SMS) for multiple chaotic systems with unknown parameters and disturbances. Both multiple coupled systems and uncoupled systems are considered. For multiple uncoupled chaotic systems (MUCSs), the sliding mode control scheme is designed to ensure that multiple response systems synchronize with one drive system under the effects of external disturbances, and the appropriate adaptive laws are proposed to estimate unknown parameters. For multiple coupled chaotic systems (MCCSs), the definition of transmission synchronization is given first. Furthermore, a special integral sliding surfaces is selected, and the corresponding controllers with the compensation terms are developed to realize SMS between every drive chaotic system and every respond system in transmission mode. Finally, some numerical examples are presented to illustrate the validity of theoretical results.

There are many behaviors with spatio-temporal characteristics in nature. Complex spatio-temporal networks (CSNs)-based on partial differential equations are to process such issues. This paper studies two synchronization boundary control methods. An adaptive boundary controller is first studied to ensure synchronization of the CSNs. Furthermore, a pinning adaptive boundary controller is proposed to achieve synchronization of the CSNs. Two sufficient criteria of synchronization and pinning synchronization are respectively obtained. Finally, two numerical examples demonstrate the effectiveness of the proposed theoretical results.

This paper studies boundary control for exponential stabilization for a distributed parameter system, modeled by semi-linear parabolic partial integro-differential equations (PIDEs) in a 1-D spatial domain. A boundary controller based on boundary measurement is designed for exponential stabilization of the PIDE system, and it is implemented by controlling and measuring only one endpoint of the 1-D spatial domain. With the Lyapunov direct method and Wirtinger’s inequality, a sufficient condition for exponential stabilization of the PIDE system with a given decay rate is investigated. Dealing with a special case of PIDE systems, one lemma called Yang inequality is proposed, and a new less conservative sufficient condition is investigated. An example with two cases is given to show the effectiveness and less conservativeness of the proposed methods by using Yang inequality.

In this paper, the almost periodic dynamical behaviors are considered for delayed complex-valued neural networks with discontinuous activation functions. We decomposed complex-valued to real and imaginary parts, and set an equivalent discontinuous right-hand equation. Depended on the differential inclusions theory, diagonal dominant principle, non-smooth analysis theory and generalized Lyapunov function, sufficient criteria are obtained for the existence uniqueness and global stability of almost periodic solution of the equivalent delayed differential system. Especially, we derive a series of results on the equivalent neural networks with discontinuous activations and periodic coefficients or constant coefficients, respectively. Finally, we give one numerical example to demonstrate the effectiveness of the derived theoretical results.

There is spatio-temporal nature for many multi-agent systems such as infight hose-and-drogue aerial refuelling systems. To deal with consensus control of such cases, this study establishes a non-linear leader-following spatio-temporal multi-agent system modelled by partial differential equations. Initially, a boundary controller based on boundary coupling is studied to ensure consensus of the multi-agent system. A sufficient condition on the existence of the controller for consensus is presented in terms of linear matrix inequalities. To simplify the obtained result, a second boundary controller is studied and a simple sufficient condition of its existence is investigated. Finally, two numerical examples demonstrate the effectiveness of the proposed methods. The merits of the proposed controllers lie in making use of only spatial boundary communication and requiring actuators and sensors only at spatial boundary positions.

This paper investigates two classes of synchronization problems of multiple chaotic systems with unknown uncertainties and disturbances by employing sliding mode control. Modified projective synchronization and transmission synchronization are discussed here. For the modified projective synchronization problem, sliding mode controllers are designed to ensure that multiple response systems synchronize with one drive system under the effects of external disturbances. For the transmission synchronization problem, based on adaptive sliding mode control, an integral sliding surface is selected and the adaptive laws are derived to tackle unknown uncertainties and disturbances for such systems. A class of nonlinear adaptive sliding mode controllers is developed to guarantee asymptotical stability of the error systems so that all chaotic systems can synchronize with each other. Simulation results are given to illustrate the effectiveness of the proposed schemes by comparing with the existing methods.

This paper mainly investigates finite-time synchronization of multiple different-order chaotic systems. Two kinds of different network synchronization modes are considered here, and the definitions of finite-time synchronization errors are given for such systems by constructing the proper vectors mapping functions. On the basis of finite-time control idea, the synchronization schemes are developed to ensure the asymptotical stability of two classes of different error systems in finite-time. Afterward, two numerical examples are calculated and simulated to illustrate the effectiveness and feasibility of proposed strategies.

This paper addresses the problem for output synchronization of a class of complex networks (CNs) with reaction–diffusion terms and input constraint. Without considering input constraint, proportional–spatial derivative (P–sD) control of the CN is firstly studied, and then, the problem of output synchronization of CN is formulated as the feasibility problem of linear matrix inequalities (LMIs). Based on the obtained results, considering P–sD control with input constraint, output synchronization is then studied and formulated as the feasibility problem of LMIs and spatial algebraic linear matrix inequalities (SALMIs). In the end, numerical simulation shows the effectiveness of the proposed methods.

The target of this article is to study almost periodic dynamical behaviors for complex-valued recurrent neural networks with discontinuous activation functions and time-varying delays. We construct an equivalent discontinuous right-hand equation by decomposing real and imaginary parts of complex-valued neural networks. Based on differential inclusions theory, diagonal dominant principle and nonsmooth analysis theory of generalized Lyapunov function method, we achieve the existence, uniqueness and global stability of almost periodic solution for the equivalent delayed differential network. In particular, we derive a series of results on the equivalent neural networks with discontinuous activation functions, constant coefficients as well as periodic coefficients, respectively. Finally, we give a numerical example to demonstrate the effectiveness and feasibility of the derived theoretical results.

We study the finite-time stability of genetic regulatory networks with impulsive effects. Using the method of Lyapunov function, sufficient conditions of the finite-stability, in terms of linear matrix inequalities, are established. A numerical example is provided to further illustrate the significance of our results.

In this paper, the authors consider the adaptive event-triggered consensus problem for a class of unknown second-order nonlinear multi-agent systems. The adaptive event-triggered controller does not rely on the global topology information of multi-agent systems, and can deal with the unknown nonlinearities of system dynamics. Unlike previous related works, our adaptive event-triggered consensus controller is firstly designed for unknown second-order nonlinear multi-agent systems. Benefiting from the event-triggered strategy, the multi-agent systems do not need continuous communications and save the bandwidth and energy resources. Finally, a simulation example is given to illustrate the effectiveness of our consensus protocol.

In this paper, we employ an efficient numerical method to solve transport equations with given boundary and initial conditions. By the weighted-orthogonal Chebyshev polynomials, we design the corresponding basis functions for spatial variables, which guarantee the stiff matrix is sparse, for the spectral collocation methods. Combining with direct algebraic algorithms for the sparse discretized formula, we solve the equivalent scheme to get the numerical solutions with high accuracy. This collocation methods can be used to solve other kinds of models with limited computational costs, especially for the nonlinear partial differential equations. Some numerical results are listed to illustrate the high accuracy of this numerical method.

// Wenyi Wu 1, * , Liting Zhang 2, * , Jianqing Lin 1 , Hanwei Huang 3 , Bai Shi 1 , Xingong Lin 1 , Zhongxin Huang 1 , Chaoyang Wang 1 , Jianlong Qiu 4 , Xiaolong Wei 5 1 Department of general surgery, The Second Affiliated Hospital of Fujian Medical University, Quanzhou, Fujian, China 2 Endocrine Department, The 180th Military Hospital of Chinese Peoples, Liberation Army, Quanzhou, Fujian, China 3 Endocrine Department, Affiliated Zhongshan Hospital of Guangdong Medical College, Zhongshan, Guangdong, China 4 Department of Pathology, The Second Affiliated Hospital of Fujian Medical University, Quanzhou, Fujian, China 5 Department of Pathology, Cancer Hospital of Shantou University Medical College, Shantou, Guangdong, China * These authors contributed equally to this work Correspondence to: Xiaolong Wei, email: weixiaolonghh@126.com Wenyi Wu, email: wwyii8522858@163.com Keywords: HIC1, SIRT1, papillary thyroid carcinoma, promoter hypermethylation Received: April 21, 2016 Accepted: October 21, 2016 Published: October 26, 2016 ABSTRACT Hypermethylation leading to the loss of hypermethylated in cancer-1 (HIC1) gene expression occurs in many different types of human cancer. HIC1 is a transcriptional repressor that directly binds to the promoter region of NAD-dependent deacetylase sirtuin-1 (SIRT1). SIRT1 functions in cell growth, is anti-apoptotic, protect neurons, functions in senescence, and regulates energy restriction. Epigenetic modification and dysregulation affecting the HIC1/SIRT1 axis is potentially important for the development of malignancies. However, the importance of HIC1 expression in the development of papillary thyroid carcinoma, especially in Chinese patients, is uncertain. Therefore, we assessed the level of methylation in the HIC1 promoter and the mRNA and protein expression levels of HIC1 and SIRT1 in human thyroid papillary carcinoma and tumor adjacent control tissues. The demethylation reagent 5-aza-2′-deoxyctidine (5-aza-dc) and an HIC1 overexpression plasmid were used to manipulate the HIC1/SIRT1 pathway, and the effects on cell senescence, apoptosis, and cell cycle progression were assessed. Compared to normal thyroid tissue, thyroid tumors had lower expression of HIC1 and higher SIRT1 expression. The level of HIC1 methylation was also higher in thyroid carcinoma tissues than adjacent tissues. HIC1 expression was closely correlated with patient age and tumor progression. Restoration of HIC1 expression through an overexpression plasmid or 5-aza-dC treatment reduced SIRT1 expression and cell proliferation, and led to senescence, cell cycle arrest, and apoptosis. Aberrant expression of HIC1/SIRT1 and hypermethylation of the HIC1 promoter may be critical for the development and progression of papillary thyroid cancer.

This paper mainly addressed the stability analysis and the estimation of domain of attraction for the endemic equilibrium of a class of susceptible-exposed-infected-quarantine epidemic models. Firstly, we discuss the global stability of the disease-free equilibrium and the local stability of the endemic equilibrium in the feasible region D of the epidemic model, respectively. Secondly, we use a geometric approach to investigate the global stability of the endemic equilibrium in a positive invariant region $$D_s(\subset D)$$ . Furthermore, we estimates the domain of attraction for the endemic equilibrium via sum of squares optimization method, and obtain the optimal estimation by solving an semidefinite programming problem with sum of squares polynomial constraints. Finally, numerical simulation is examined to demonstrate the feasibility and effectiveness of the research results.

This paper addresses the problem of exponential stability and stabilization for a class of delayed distributed parameter systems, which is modeled by partial integro-differential equations (PIDEs). By employing the vector-valued Wirtinger’s inequality, the sufficient condition of exponential stability of the PIDE system with a given decay rate is investigated. The condition is presented by linear matrix inequality (LMIs). After that, we develop a spatial proportional-integral-derivative state-feedback controller that ensures the exponential stabilization of the PIDE system in terms of LMIs. Finally, numerical examples are presented to verify the effectiveness of the proposed theoretical results.

Inertia wheel pendulum (IWP) is a typical underactuated nonlinear mechanical system. This paper concerns the stabilizing control problem for this nonlinear system. A control strategy based on coordinate transformation and time reverse is presented. The proposed strategy consists of three steps. First, a coordinate transformation is constructed for the IWP. It changes the IWP into a cascade nonlinear system and transforms the stabilization of the IWP into that of the cascade system. Second, the dynamics of the cascade system is analyzed and a time-reverse strategy is used to construct a trajectory for the cascade system. After that, two methods of designing controller for the cascade system are developed to track the constructed trajectory. It ensures the stabilizing control of the cascade system to be achieved. And thus, the stabilization control objective of IWP is realized. In order to test the validity of our proposed theoretical results, a numerical example is given finally. The simulation results demonstrate its effectiveness and its superiority over others.

In this paper, we investigate the hybrid synchronization behavior in an array of coupled chaotic systems with ring connection, of which means complete synchronization (CS) and anti-synchronization (AS) could coexist. First, the anti-synchronization controllers are designed, which can transform the synchronization error dynamic system into a nonlinear system with an antisymmetric structure. Second, we investigate the complete synchronization behavior in such a chaotic system under the anti-synchronization control. After that, the stability conditions are given for reaching hybrid synchronization. Finally, numerical examples and simulation results are presented to verify and validate the hybrid synchronization behavior in coupled chaotic system. HighlightsWe study the hybrid synchronization of multiple coupled chaotic systems with ring connection.In our chaotic systems model, we can avoid the occurrence of a fault to reach the synchronization.The new stability conditions are given for reaching hybrid synchronization.The controller designed can transform the synchronization error system as a simple nonlinear system.Research results will undoubtedly improve the performance of multilateral communications.

In this paper we study the quasineutral limit of the two-species Vlasov-Poisson system. For well-prepared initial data, we establish the convergence of the Vlasov-Poisson system to the pressureless Euler system as the Debye length tends to zero.

In this paper, we use an underactuated four-link gymnast robot (UFGR) with a passive first joint to model a gymnast on the bar, and consider the stabilization of the UFGR at the straight-up position. First, we introduce a coupled relationship between control torques for the UFGR. It decouples some state variables of the UFGR from others and changes the nonlinear UFGR system into a cascade-connected system. And then, we use an energy-based method to design a stabilizing controller for the zero dynamics of the cascade-connected system. And the triangle lemma guarantees the control objective of the UFGR to be achieved. The torque-coupled method transforms the stabilization of an underactuated four-link manipulator into that of an underactuated two-link acrobot. This makes the structure of the control system simple. Moreover, our proposed control strategy is easy to extend to the stabilization control of other multi-input nonlinear underactuated systems. Simulation results using the characteristics parameters of a gymnast demonstrate the validity of the proposed method.

For a lithium battery, a gated recurrent unit recurrent neural network (GRU-RNN) based momentum gradient method is investigated to estimate its state of charge (SOC). In the momentum gradient method, the current weight change direction takes a compromise of the gradient direction at current instant and at historical time to prevent the oscillation of the weight change and to improve the SOC estimation speed. The details include: (1) construct a GRU-RNN model for estimating SOC by taking the measured voltage and current as the inputs, and the estimated SOC as the output of the GRU-RNN; (2) to promote the SOC convergence speed, explore the momentum gradient algorithm to optimize the weights of the network by introducing a momentum term; (3) to prevent overfitting and to improve generalization ability of the GRU-RNN model, add noises to the sample data, so as to improve the SOC estimation accuracy; (4) set up a lithium battery test platform to sample data in battery discharge process and to implement MATLAB simulation. The simulation results verify that the momentum optimized GRU-RNN model can accurately and effectively estimate the SOC of the lithium battery.

This paper focuses on exponential synchronization for master-slave time-varying delayed complex-valued neural networks (CVNNs) under hybrid impulsive controllers. Hybrid impulsive controllers is the extension of impulsive controllers, which can simultaneously permit synchronizing as well as desynchronizing impulses in one impulsive sequence, i.e., hybrid impulses. We separate CVNNs into their real and imaginary parts, which leads to two real-valued neural networks (RVNNs). Based on the concepts of average impulsive interval (AII) and average impulsive gain (AIG), we find that master-slave exponential synchronization for the real and imaginary parts of CVNNs can be realized via hybrid impulsive control under certain conditions. By employing the Lyapunov method, sufficient criteria are established to guarantee synchronization of the given master-slave CVNNs. Finally, the validity of the obtained results is demonstrated via a numerical example.

In this paper, a cyber-physical system under attack is modeled by a descriptor system with unknown inputs. By partitioning the descriptor system into several disjoint areas, we build a drive-response descriptor system and discuss the adaptive control problem in different situations based on Lyapunov stability theory. First, parameter update laws are presented to identify the unknown system parameters. Second, adaptive controllers are designed to deal with the problem of outer synchronization between the drive system and the response system. Third, it is proved that the effects of unknown inputs and time-varying delays are compensated by the adaptive controllers. Finally, several numerical simulations are carried out to illustrate the effectiveness of the update laws and adaptive controllers.

The output signal of the rotating accelerometer gravity gradiometer instrument (GGI) is extremely complicated in the real gravity gradient measurement environment. Many kinds of perturbations and noises are unavoidable in real GGI systems, among all the various errors, the inconsistency of scale factors has a great influence on the resolution of the rotating accelerometer gravity gradiometer. To reduce this specific error, this paper presents a new algorithm to adjust the accelerometer scale factor. First, the band-passing filter was adopted to filtrate the output of the two opposing accelerometers. Then, the signal was demodulated from the output of the band-passing filter. This processing method is the same to the output signal of the other pair of accelerometers and the total output signal of GGI. With the three demodulation results, smoothing filtering method and real time PID feedback algorithm were used to adjust the accelerometer internal torque coils to adjust the scale factor in time. Finally, by using the method proposed in this paper, the experiment results verify that the inconsistency of the scale factor of four accelerometers on GGI was dramatically improved and the precision of gradient signal is further improved.

Ahstract- This paper concerns the properties analysis and motion planning for an underactuated wheeled Acrobot (WAcrobot). First, an input relationship is constructed based on the structural characteristics of the WAcrobot system, which changes the system into a nonlinear cascade system. And the dynamic properties of the cascade system are analyzed. After that, the properties and a reverse motion idea are used to design a motion trajectory for the WAcrobot in its whole motion space. The trajectory starts from a stable equilibrium point and ends at an unstable equilibrium point of the system. Tracking the trajectory enables the swing-up and stabilization control objective of the WAcrobot to be achieved. Finally, a numerical example demonstrates the effectiveness of our presented theoretical results.

We investigate cluster-delay synchronization of a directed network possessing cluster structures by designing an intermittent control protocol. Based on Lyapunov stability theory, we proved that synchronization can be realized for oscillators in the same cluster and cluster-delay synchronization can be realized for the whole network. By simplifying the obtained sufficient conditions, we carry out a succinct and utilitarian corollary. In addition, comparative researches are carried out to show the differences and the usefulness of the obtained results with respect to other similar controllers from the recent literature. Finally we provide two numerical examples to show the effectiveness of the control schemes.

Motivated by the quorum-sensing mechanism of bacteria, this paper modifies the network model by adding unknown parameters and noise disturbances and investigates the problem of outer synchronization via adaptive control. In case there exist three unknown parameters, updating laws are presented to identify the unknown parameters with help of Lyapunov stability theory, and the negative effects of noise disturbances are also compensated by designing adaptive controllers. In addition, we simplify the obtained conditions and carry out two succinct and utilitarian corollaries. Finally, numerical simulations are provided to show the validity of the obtained results.

This paper concerns the motion trajectory design for an underactuated three-link robot (UTGR). First, we design a controller for the UTGR system based on the system's dynamic structure characteristics. And then, the properties of closed-loop system are analyzed. After that, a motion trajectory of the UTGR is designed based on the analyzed properties and an inverted trajectory idea. The designed trajectory starts from the downward position and ends at the upward position. Tracking of this trajectory can enable the stabilization control objective of UTGR from the downward position to the upward position to be achieved. A numerical example demonstrates the effectiveness of our proposed theoretical results.

In this paper, we study the synchronization problem for switched complex networks with delayed coupling via semi-periodically intermittent control technique and a mode-dependent average dwell time method. The mathematical model of switched complex networks is established, and the networks switch among a finite number of subnetworks in accordance with a switching rule. By applying multiple Lyapunov function method and the mode-dependent average dwell time (MDADT) approach, less conservative synchronization criteria are derived based on a sequence of solvable linear matrix inequalities. Particularly, the conventional synchronization conditions are improved by using semi-periodically intermittent control and MDADT approach. Moreover, delayed coupling may affect the stability of the switched complex networks. In this paper, novel synchronization criteria are derived to deal with the relations between time delay and other parameters appropriately. Finally, a numerical example is provided to demonstrate the effectiveness of the derived theoretical results.

This paper concerns the p th moment synchronization in an array of generally coupled memristor-based neural networks with time-varying discrete delays, unbounded distributed delays, as well as stochastic perturbations. Hybrid controllers are designed to cope with the uncertainties caused by the state-dependent parameters: (a) state feedback controllers combined with delayed impulsive controller; (b) adaptive controller combined with delayed impulsive controller. Based on an impulsive differential inequality, the properties of random variables, the framework of Filippov solution, and Lyapunov functional method, sufficient conditions are derived to guarantee that the considered coupled memristor-based neural networks can be p th moment globally exponentially synchronized onto an isolated node under both of the two classes of hybrid impulsive controllers. Finally, numerical simulations are given to show the effectiveness of the theoretical results.

This paper addresses the problem of exponential synchronization for a class of complex spatio-temporal networks with space-varying coefficients, where the dynamics of nodes are described by coupled partial differential equations (PDEs). The goal of this research is to design distributed proportional-spatial derivative (P-sD) state feedback controllers to ensure exponential synchronization of the complex spatio-temporal network. Using Lyapunov׳s direct method, the problem of exponential synchronization of the complex spatio-temporal network is formulated as the feasibility problem of spatial differential linear matrix inequality (SDLMI) in space. The feasible solutions to this SDLMI in space can be approximately derived via the standard finite difference method and the linear matrix inequality (LMI) optimization technique. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed design method.

This paper studies the existence and stability of periodic solution of the high-order discrete-time Cohen–Grossberg neural networks with varying delays. The properties of M-matrix and the contracting mapping principle are used to obtain a sufficient condition that guarantees the uniqueness and global exponential stability of the periodic solution. In addition, a numerical example is given that demonstrates the effectiveness of the proposed theoretical results.

This paper discusses the problem for cluster synchronization control of a nonlinear complex spatio-temporal dynamical network (CSDN) with community structure. Initially, a collocated boundary controller with boundary measurement is studied to achieve the cluster synchronization of the CSDN. After that, a guaranteed cost boundary controller is further developed based on the obtained results. Furthermore, the suboptimal control design is addressed by minimizing an upper bound of the cost function. Finally, a numerical example is given to demonstrate the effectiveness of the proposed methods.

This paper studies the transmission synchronization (TS) problem among multiple coupled chaotic systems by considering unknown parameters. In the solving process, we firstly select a special integral sliding surfaces, and then we develop an effective controller with the compensation terms to guarantee the asymptotical stability of all TS error systems. Simultaneously, we design the proper adaptive laws to estimate all unknown parameters. Finally, numerical example is used to show the effectiveness of the proposed schemes.

This paper studies boundary control for function projective synchronization of a complex sptio-temporal network with time-varying delays and nonlinear terms satisfying the Lipschitz condition. A boundary controller based on distributed measures is studied for function projective synchronization. Using Lyapunov's direct method, the problem of existence of the controller is formulated as the feasibility problem of linear matrix inequalities (LMIs). Finally, an example shows the effectiveness of the proposed method.

This paper proposes an anti-hepatitis B virus (HBV) infection treatment model with an immune response term and an alanine aminotransferase (ALT) term. This model has five variables, which can be used to describe the evolution dynamics of the related clinical data of the chronic hepatitis B (CHB) patients. We use this model to simulate the dynamics of evolutions of serum HBV DNA levels and ALT levels of 115 CHB patients, who had been taking Tenofovir Disoproxil Fumarate (TDF) for 48 weeks. The results show that TDF has higher therapeutic efficacy and causes viral mutation at very low levels, and TDF anti-HBV infection treatment can activate the patients' two kinds of immunity to remove HBV by different ways.

In this paper, we address the finite-time tracking consensus control problem for nonlinear multi-agent systems under no-cycle communication graph. Unlike most existing works of finite-time consensus, we focus on nonlinear multi-agent systems with lower triangular subsystems. Based on the local cooperative information among neighboring agents, we propose a tracking consensus protocol ensuring that all agents achieve consensus in a finite time. Finally, we give an example to illustrate the effectiveness of the proposed protocols.

This paper deals with the problem of complex spatio-temporal networks, which is modeled by coupled partial integro-differential equations (PIDEs). A spatial proportional-integral-derivative (SPID) state-feedback controller is studied. With Laypunov direct method, a sufficient condition on synchronization of the complex PIDE network is investigated in terms of linear matrix inequality (LMIs). Finally, a numerical example shows the effectiveness of the proposed results.

This paper analyzes multi-switching network transmission synchronization (MSNTS) problem among three uncertain chaotic systems with unknown parameters. By constructing the effective switching rules, the definition of MSNTS is given and the synchronization schemes are proposed to reach synchronization between any different states of each derive system and any desired states of every respond system by choosing the proper transmission path. Finally, simulation results show the feasibility of research results.

This paper is concerned with the state estimation problem of BAM neural networks with mixed time delays. By constructing a suitable Lyapunov-Krasovskii functional (LKF), a new criterion is obtained so that the BAM neural networks error system is asymptotically stable. A simulation example is given to demonstrate the effectiveness of the proposed method.

In this paper, finite-time synchronization (FTS) problems in an array of unified chaotic and hyperchaotic systems are mainly studied using some important control methods. First, FTS and finite-time transmission synchronization (FTTS) for N systems are realized in a finite time by designing the effective control schemes, and the stability criteria can be given. The corresponding examples are presented to show the effectiveness and feasibility of the controllers proposed by considering three chaotic and hyperchaotic systems.

The authors study the second-order finite-time coordination problems of nonlinear multi-agent systems with directed graph. By using the homogeneous theories, we firstly give a finite-time coordination controller for the leaderless multi-agent system. Then, another finite-time controller for leader-follower multiagent system was given. Finally, the authors give a simulation, which shows the effectiveness of the given finite-time coordination controllers.

This paper addresses the problem of robustH∞control design via the proportional-spatial derivative (P-sD) control approach for a class of nonlinear distributed parameter systems modeled by semilinear parabolic partial differential equations (PDEs). By using the Lyapunov direct method and the technique of integration by parts, a simple linear matrix inequality (LMI) based design method of the robustH∞P-sD controller is developed such that the closed-loop PDE system is exponentially stable with a given decay rate and a prescribedH∞performance of disturbance attenuation. Moreover, a suboptimalH∞controller is proposed to minimize the attenuation level for a given decay rate. The proposed method is successfully employed to address the control problem of the FitzHugh-Nagumo (FHN) equation, and the achieved simulation results show its effectiveness.