Kai-Ning Wu

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• PhD
• Professor at Harbin Institute of Technology

The boundary stabilization of a class of reaction-diffusion systems perturbed by second-order processes is investigated in this work. It extends the results from random ordinary differential equations to random reaction-diffusion systems (RRDSs). First, the stability analysis of RRDSs with boundary function is presented. Using the Lyapunov method a...

Fault detecting is crucial for the safety of the lithium-ion battery. This is because thermal fault and sensor fault are the most common fault in battery, and it may be catastrophic. This study explores a novel fault detection scheme for the cylindrical lithium-ion battery. In this scheme, for the modeling simplicity and physical realism, an electr...

This work investigates the observer-based asynchronous boundary stabilization for a kind of stochastic Markovian reaction–diffusion neural networks with exogenous disturbances. Specifically, parameter uncertainties are considered in the drift item. First, a hidden Markov model is introduced that guarantees the observer modes run asynchronously with...

The passivity‐based boundary control is considered for stochastic Korteweg–de Vries–Burgers (SKdVB) equations. Both the stochastic input strictly passive (SISP) and stochastic output strictly passive (SOSP) are studied. By introducing Lyapunov functionals and Wirtinger's inequality, sufficient criteria are derived to establish SISP and SOSP for SKd...

This paper considers the interval estimation for delayed linear reaction-diffusion systems. To obtain the estimates of the states for delayed reaction-diffusion systems, a novel interval estimation scheme is proposed based on a spatial finite difference method and decoupling technology. First, the delayed reaction-diffusion system is discretized by...

The robust exponential stabilization is addressed for uncertain delay reaction-diffusion systems (UDRDSs) via sliding mode boundary control (SMBC). Firstly, a novel integral sliding mode surface (SMS) is proposed, on which system states slide to the equilibrium with an exponential convergence rate. Furthermore, the sliding mode boundary controller...

This paper mainly analyzes the finite-time stabilization of semi-Markov reaction-diffusion memristive neural networks (R-DMNNs) with unbounded time-varying delays. Firstly, the reaction-diffusion term and semi-Markov jumping are introduced into memristive neural networks, which relaxes the limitation of Markov switching on sojourn time and makes th...

The exponential input-to-state stability (EISS) is studied for delay Korteweg–de Vries–Burgers (DKdVB) equations. DKdVB equations are considered with distributed input and boundary input. Making use of the Lyapunov–Krasovskii functional method and inequality techniques, a sufficient condition is established to ensure the EISS for DKdVB equations. B...

This paper considers the problem of the boundary fixed-time stabilisation for delay reaction–diffusion systems (DRDSs). A new boundary controller is designed to achieve fixed time stability of DRDSs. Firstly, a boundary fixed-time controller is presented for DRDSs. Then based on the designed boundary controller, using Lyapunov functional method, fi...

This article studies the synchronization of new coupled fractional delayed reaction–diffusion neural networks with reaction terms satisfying the global Lipschitz condition via time-continuous and time-discontinuous boundary controllers. The realization of neural networks inevitably involves diffusion phenomena and time delays, and all the neurons o...

This paper investigates the boundary finite‐time stabilization of fractional reaction‐diffusion systems (FRDSs). First, a distributed controller is designed, and sufficient conditions are obtained to ensure the finite‐time stability (FTS) of FRDSs under the designed controller. Then, a boundary controller is presented to achieve the FTS. By virtue...

This paper considers the passivity-based boundary control for stochastic delay reaction–diffusion systems (SDRDSs) with boundary input–output. Delay-dependent sufficient conditions are obtained in the sense of expectation for SDRDSs by the use of Lyapunov functional method, for the input strict passivity and the output strict passivity, respectivel...

The finite-time boundary stabilization is investigated for Korteweg-de Vries-Burgers (KdVB) equations. Firstly, a distributed controller is derived, and criteria are presented to guarantee the finite-time stability (FTS) of KdVB equations via the distributed controller. Then, considering the installation in real applications, a vogue control strate...

Exponential stability is considered for delay reaction–diffusion cellular neural networks (DRDCNNs) under two cases where the state information is fully available and not fully available. When the state information of controlled system is fully available, an aperiodically intermittent boundary controller is designed to stabilize the controlled syst...

The boundary control problem is considered for stochastic Korteweg-de Vries-Burgers equations. First, a boundary controller is proposed, and a criterion is obtained for mean square exponential stability by using the Lyapunov functional method and inequality techniques. Then, when there exist uncertainties in the system parameters, the robust mean s...

Passivity-based boundary control is considered for time-varying delay reaction-diffusion systems (DRDSs) with boundary input-output. By virtue of Lyapunov functional method and inequality techniques, sufficient conditions are obtained for input strict passivity and output strict passivity of DRDSs, respectively. When the parameter uncertainties app...

This article concerns with the asynchronous boundary control for a class of Markov jump reaction-diffusion neural networks (MJRDNNs). In consideration of nonsynchronous behavior between the system modes and controller modes, a novel asynchronous boundary control design is proposed for MJRDNNs. Based on the designed asynchronous boundary controller,...

This paper deals with the exponential boundary stabilization for a class of Markov jump reaction-diffusion neural networks (MJRDNNs) with mixed time-varying delays, which is described by T-S fuzzy model. It is assumed that observed modes in boundary controller are not synchronized with the system modes. Based on a hidden Markov model (HMM), a novel...

The boundary control problem is considered for stochastic Korteweg-de Vries-Burgers equations. First, a boundary controller is proposed, and a criterion is obtained for mean square exponential stability by using Lyapunov functional method and inequality techniques. Then, when there exist uncertainties in the system parameters, the robust mean squar...

This paper investigates the boundary finite-time stabilization of fractional reaction-diffusion systems (FRDSs). First, a distributed controller is designed, and sufficient conditions are obtained to ensure the finite-time stability (FTS) of FRDSs under the designed controller. Then, a boundary controller is presented to achieve the FTS. By virtue...

Dissipativity-based asynchronous boundary stabilization problem is addressed for stochastic Markov jump reaction-diffusion systems (SMJRDSs). In practical engineering, nonsynchronous behavior between system modes and controller modes is inevitable, and the incomplete matrix information makes the problem analysis difficult, so this work considers th...

The finite-time control is considered for reaction–diffusion systems (RDSs) under a designed spatial sampled-data controller (SSDC). Firstly, an SSDC is designed and the finite-time stability is investigated for RDSs, based on the designed controller. In terms on Lyapunov functional method and inequality techniques, a sufficient condition is obtain...

This article considers the exponential stabilization and H∞ performance for delay reaction‐diffusion systems (DRDSs), with spatial sampled‐data controller (SSDC) and spatio‐temporal sampled‐data controller (STSDC). Firstly, an SSDC is designed to stabilize the DRDSs. Using Lyapunov functional and Wirtinger's inequality technique, we obtain sufficie...

Exponential stabilization is studied for reaction-diffusion systems (RDSs) with a reaction term satisfying the global Lipchitz condition by means of intermittent boundary control. First, a state-dependent intermittent boundary controller is designed when system states are available. By employing the spatial integral functional method and Poincares...

This article mainly deals with observer‐based H∞ control problem for a stochastic Korteweg–de Vries–Burgers equation under point or averaged measurements. Due to the nonlinearity of the stochastic partial differential equations, special emphases are given to computation complexity. By constructing an appropriate Lyapunov functional, we derive suffi...

This brief paper considers the exponential input-to-state stability (EISS) for delay reaction-diffusion systems (DRDSs). The distributed input and boundary input are both included in the considered model. Boundary input is an important characteristic for DRDSs which are a kind of partial differential systems. Using Lyapunov–Krasovskii functional me...

This study considers the boundary stabilization for stochastic delayed Cohen-Grossberg neural networks (SDCGNNs) with diffusion terms by the Lyapunov functional method. In the realization of NNs, sometimes time delays and diffusion phenomenon cannot be ignored, so Cohen-Grossberg NNs with time delays and diffusion terms are studied in this article....

This paper investigates the finite-time stability (FTS) for a class of stochastic Markovian reaction-diffusion systems (SMRDSs). First, a boundary control strategy is put forward. Under the designed boundary controller, a sufficient condition of FTS for SMRDSs is provided based on the method of Lyapunov-Krasovskii functional combined with inequalit...

This paper considers the control problems for stochastic reaction-diffusion systems (SRDSs) with a spatial sampled-data (SSD) controller. The SSD controller engenders spatial discrete term such that the SRDS with SSD controller is a hybrid system. The coexistence of stochastic disturbance, spatial diffusion and discrete term brings out new challeng...

Mittag-Leffler stabilization is studied for fractional reaction-diffusion cellular neural networks (FRDCNNs) in this paper. Different from previous literature, the FRDCNNs in this paper are high-dimensional systems, and boundary control and observed-based boundary control are both used to make FRDCNNs achieve Mittag-Leffler stability. First, a stat...

Cohen-Grossberg neural networks (CGNNs) play an important role in many applications and the stabilization of this system has been well studied. This study considers the exponential stabilization for stochastic reaction–diffusion Cohen-Grossberg neural networks (SRDCGNNs) by means of an aperiodically intermittent boundary control. Both SRDCGNNs with...

This paper considers the mean square exponential input-to-state stability (EISS) for stochastic delay reaction-diffusion neural networks (SDRDNNS). SDRDNNS with distributed input and boundary input are investigated. In addition, constant delay and time-varying delay are considered. With the help of Lyapunov-Krasovskii functional method, Itô formula...

This article focuses on the boundary control of stochastic Markovian reaction‐diffusion systems (SMRDSs). Both the cases of completely known and partially unknown transition probabilities are taken into account. By using the Lyapunov functional method, a sufficient condition is obtained under the designed boundary controllers to guarantee the asymp...

This paper considers the finite-time stability of impulsive reaction-diffusion systems (IRDSs). We deal with two cases, systems without time delay and systems with time delay. When there is no delay in the considered system, we obtain sufficient conditions to guarantee the finite-time stability of IRDSs via two representations of impulsive sequence...

We consider the finite-time synchronisation for coupled reaction-diffusion systems. At first, we design a pinning control strategy for the coupled systems. For the uncontrolled nodes, we use the adaptive adjustment to the coupling strength. Based on the Poincaré inequality technique and using the finite-time stability lemma, we obtain the sufficien...

This study considers asymptotic stability in the mean square sense for stochastic delay Markovian reaction-diffusion systems (SDMRDSs) via boundary control. Firstly, the authors present a boundary controller for the system. By constructing of a Lyapunov–Krasovskii functional and utilising of Poincaré inequality, a sufficient criterion of mean squar...

This paper considers mean square finite-time synchronization for coupled impulsive stochastic delay reaction-diffusion systems (ISDRDSs). Using Lyapunov–Krasovskii functional method, impulsive comparison lemma and Gronwall’s inequality, we obtain sufficient conditions that ensure mean square finite-time synchronization of coupled ISDRDSs. These suf...

In this paper, the boundary control problem of stochastic reaction-diffusion systems (SRDSs) is studied. First, a distribution controller is designed, and a sufficient condition is established to achieve mean square finite-time stability. Then a boundary controller is proposed, and a criterion is obtained for mean square finite-time stability by us...

This paper studies the problem of mean square asymptotical synchronization and \(H_\infty \) synchronization for coupled stochastic reaction–diffusion systems (SRDSs) via boundary control. Based on the deduced synchronization error dynamic, we design boundary controllers to achieve mean square asymptotical synchronization. By virtue of Lyapunov fun...

This paper considers the boundary control problem for linear stochastic reaction‐diffusion systems with Neumann boundary conditions. First, when the full‐domain system states are accessible, a boundary control is designed, and a sufficient condition is established to ensure the mean‐square exponential stability of the resulting closed‐loop system....

This paper considers finite-time stabilization and H∞ performance for delay reaction–diffusion systems by boundary control. First, a full-domain controller is designed and sufficient conditions are obtained to achieve finite-time stability using finite-time stability lemma and Wirtinger's inequality method. Then a boundary controller furnished with...

In this paper, the problem of boundary finite-time stabilization is considered for reaction-diffusion systems (RDSs). First, a full-domain controller is designed and sufficient conditions are given to ensure finite-time stability of RDSs under the designed controller. Then, for practical applications, a boundary controller is designed to obtain fin...

This paper considers the cluster synchronisation of coupled delay reaction-diffusion systems (DRDSs). First, in light of the technique of matrix representation, we turn the cluster synchronisation of coupled DRDSs into the asymptotical stability of a transformed system. Based on this transformation and by virtue of the Lyapunov-Krasovskii functiona...

In this paper, we address the mixed H2/H∞ synchronization control for the coupled partial differential systems. First, we introduce the synchronization error dynamics and transform the problem of mixed H2/H∞ synchronization control of coupled partial differential systems into the problem of mixed H2/H∞ stabilization of the synchronization error dyn...

The synchronization for coupled linear partial differential systems(PDSs) with boundary control is considered. Based on the nonsingular matrix transformation method, we decouple the coupled synchronization error dynamical systems and turn the synchronization control problem into the asymptotical stabilization problem. Then, using the backstepping a...

This paper considers a stochastic logistic model with infinite delay and impulsive perturbation. Firstly, with the space Cg as phase space, the definition of solution to a stochastic functional differential equation with infinite delay and impulsive perturbation is established. According to this deinition, we show that our model has an unique globa...

This paper discusses the problems of stabilization and H∞ control for stochastic reaction-diffusion systems(SRDSs) via boundary control. The SRDSs with Neumann boundary condition is considered. Making use of the Lyapunov-Krasoviskii functional method and Ito formula, we obtain the sufficient condition guaranteeing the mean square asymptotical stabi...

The asymptotical synchronization for coupled delay partial differential systems (PDSs) with boundary control is considered in this paper. First, the synchronization error dynamics are introduced and we turn the asymptotical synchronization problem into the asymptotical stabilization problem. The boundary controller is also presented. Then, by emplo...

In this paper, the criterion and control are considered for the mean square H∞ synchronization of coupled stochastic partial differential systems (SPDSs). Based on the integral Lyapunov-like functional and by virtue of completing squares technique, a sufficient criterion is provided to guarantee the mean square H∞ synchronization. The effect of spa...

In this paper, we consider mixed H 2/H ∞ control problems for linear infinite-dimensional systems. The first part considers the state feedback control for the H 2/H ∞ control problems of linear infinite-dimensional systems. The cost horizon can be infinite or finite time. The solutions of the H 2/H ∞ control problem for linear infinitedimensional s...

This paper considers the asymptotical synchronization of coupled nonlinear impulsive partial differential systems (PDSs) in complex networks. The cases of both complex networks with fixed topology and switching topology are studied. Based on the Lyapunov–Krasoviskii functional method, sufficient conditions are presented to guarantee the asymptotica...

In this paper, the finite-time synchronization of coupled stochastic partial differential systems (SPDSs) is investigated. First, we get the synchronization error dynamics, and the finite-time synchronization problem is transformed into the finite-time stabilization problem of synchronization error dynamics. By virtue of the finite-time stability l...

This paper considers the asymptotical synchronization and \(H_\infty \) synchronization for coupled neutral-type delay partial differential systems (NDPDSs). First, we construct a coupled synchronization error dynamic. Using the method of nonsingular matrix transformation, we decouple these coupled synchronization error dynamical systems. Then we s...

This paper considers the -moment boundedness of nonlinear impulsive stochastic delay differential systems (ISDDSs). Using the Lyapunov-Razumikhin method and stochastic analysis techniques, we obtain sufficient conditions which guarantee the -moment boundedness of ISDDSs. Two cases are considered, one is that the stochastic delay differential system...

This paper considers the synchronization problem for the coupled nonlinear delay stochastic partial differential systems (SPDSs), both mean square asymptotical synchronization and mean square H infinity synchronization are studied. Making use of the Lyapunov-Krasoviskii functional method and It¨o formula, sufficient conditions are derived which gua...

Robust model predictive control with On-Off input of system is researched in this paper. The constraint tightening approach is adopted to ensure robustness of algorithm. By variable horizon approach, i.e. take the predictive horizon as the decision variable, the property of finite-time arrival within an arbitrary target set is guaranteed. Convergen...

This paper deals with the mean square convergence and mean square exponential stability of an Euler scheme for a linear impulsive stochastic delay differential equation (ISDDE). First, a method is presented to take the grid points of the numerical scheme. Based on this method, a fixed stepsize numerical scheme is provided. Based on the method of fi...

This paper considers the asymptotical synchronization and robust $H_{\infty}$ synchronization for coupled time-varying delay partial differential systems (PDSs) on complex dynamical networks. Both time-varying delay in the coupling and in the dynamical nodes are investigated. Making use of the Lyapunov-Krasoviskii functional method, sufficient cond...

This brief discusses the asymptotical synchronization and robust H∞ synchronization for coupled semilinear partial differential systems (PDSs) with time-varying delay in spatial coupling. First, using the Lyapunov-Krasoviskii functional method, sufficient conditions are obtained for the asymptotical synchronization of coupled semi-linear time-delay...

In this article, we consider the impulsive stabilization of delay difference equations. By employing the Lyapunov function and Razumikhin technique, we establish the criteria of exponential stability for impulsive delay difference equations. As an application, by using the results we obtained, we deal with the exponential stability of discrete impu...

We consider the stability and stabilization of impulsive stochastic delay differential equations (ISDDEs). Using the Lyapunov-Razumikhin method, we obtain the sufficient conditions to guarantee the pth moment exponential stability of ISDDEs. Then the almost sure exponential stability is considered and the sufficient conditions of the almost sure ex...

Aging, an extremely complex and system-level process, has attracted much attention in medical research, especially since chronic diseases are quite prevalent in the aged population. These may be the result of both gene mutations that lead to intrinsic perturbations and environmental changes that may stimulate signaling in the body. In addition, agi...

In this paper, the exponential stability of impulsive delay difference equations is studied and the stability of the Euler method is considered for a linear impulsive delay differential equation. Using the Lyapunov function and Razumikhin technique, criteria for exponential stability of impulsive delay difference equations are established. As an ap...

This paper presents a fixed stepsize Euler scheme for linear impulsive delay differential equations and considers its convergence. We propose a method to take the partition nodes for the Euler scheme. Employing the induction and the technique of inequality, we obtain the order of convergence for Euler scheme. An example is given to illustrate the e...

When an impulsive control is adopted for a stochastic delay difference system (SDDS), there are at least two situations that should be contemplated. If the SDDS is stable, then what kind of impulse can the original system tolerate to keep stable? If the SDDS is unstable, then what kind of impulsive strategy should be taken to make the system stable...

In this paper, the existence and global exponential stability of periodic solutions for a class of numerical discretization neural networks are considered. Using coincidence degree theory and the Lyapunov method, sufficient conditions for the existence and global exponential stability of periodic solutions are obtained. A numerical simulation is gi...

The exponential stability of impulsive delay difference equations is considered. Employing the Lyapunov function, some conditions are obtained which guarantee the exponential stability of impulsive delay difference equations, that are the stability criteria for the impulsive delay difference equations. For linear impulsive delay difference equation...

This paper deals with the convergence and stability of the semi-implicit Euler method for linear stochastic delay integro-differential equations. It is proved that the semi-implicit Euler method is convergent with strong order p=0.5. The condition under which the method is asymptotic mean square stable is determined and numerical experiments are pr...