Jianlong Qiu

p th moment exponential stochastic synchronization of coupled memristor-based neural networks with mixed delays via delayed impulsive control

This paper concerns the pth 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 pth 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.

Existence and global exponential stability of periodic solution for high-order discrete-time BAM neural networks

This paper concerns the existence and exponential stability of periodic solution for the high-order discrete-time bidirectional associative memory (BAM) neural networks with time-varying delays. First, we present the criteria for the existence of periodic solution based on the continuation theorem of coincidence degree theory and the Youngs inequality, and then we give the criteria for the global exponential stability of periodic solution by using a non-Lyapunov method. After that, we give a numerical example that demonstrates the effectiveness of the theoretical results. The criteria presented in this paper are easy to verify. In addition, the proposed analysis method is easy to extend to other high-order neural networks.

Finite-Time Control of Multiple Different-Order Chaotic Systems with Two Network Synchronization Modes

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.

Finite-time stability of genetic regulatory networks with impulsive effects

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.

Robust Exponential Synchronization for a Class of Master-Slave Distributed Parameter Systems with Spatially Variable Coefficients and Nonlinear Perturbation

This paper addresses the exponential synchronization problem of a class of master-slave distributed parameter systems (DPSs) with spatially variable coefficients and spatiotemporally variable nonlinear perturbation, modeled by a couple of semilinear parabolic partial differential equations (PDEs). With a locally Lipschitz constraint, the perturbation is a continuous function of time, space, and system state. Firstly, a sufficient condition for the robust exponential synchronization of the unforced semilinear master-slave PDE systems is investigated for all admissible nonlinear perturbations. Secondly, a robust distributed proportional-spatial derivative (P-sD) state feedback controller is desired such that the closed-loop master-slave PDE systems achieve exponential synchronization. Using Lyapunov’s direct method and the technique of integration by parts, the main results of this paper are presented in terms of spatial differential linear matrix inequalities (SDLMIs). Finally, two numerical examples are provided to show the effectiveness of the proposed methods applied to the robust exponential synchronization problem of master-slave PDE systems with nonlinear perturbation.

Transmission Synchronization Control of Multiple Non-identical Coupled Chaotic Systems

In this paper, we investigate the transmission projective synchronization control problem for multiple, non-identical, coupled chaotic systems. By considering the influence of the occurrence of a fault between a driving system and a responding system, we define our new transmission synchronization scheme. After that, control laws are designed to achieve transmission projective synchronization and a simple stability criteria is obtained for reaching the transmission synchronization among multi-systems. A numerical example is used to verify the effectiveness of the synchronization within a desired scaling factor.

Guaranteed cost boundary control for cluster synchronization of complex spatio-temporal dynamical networks with community structure

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.

Stability and stabilization of a delayed PIDE system via SPID control

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.

Robust Tracking Control of Robot Manipulators Using Only Joint Position Measurements

This paper concerns the tracking control of a robot manipulator with unknown uncertainties and disturbances. It presents a new control method that uses only joint position measurements to design a tracking controller. The controller has two parts. One is based on a feedback linearization technique; it makes the nominal model of a manipulator asymptotically track a desired trajectory. The other is based on the idea of equivalent input disturbance (EID); it compensates for uncertainties and disturbances. Together they enable a robot manipulator to precisely track the desired trajectory. The new control algorithm is applied to a two-link robot manipulator, and simulation results demonstrate the validity of this method.

Finite-time coordination of a class of second-order nonlinear multi-agent 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.