Sampled-Data Synchronization of Stochastic Markovian Jump Neural Networks With Time-Varying Delay

A Sliding Mode Control Method With Variable Convergence Rate for Nonlinear Impulsive Stochastic Systems

This article addresses the variable convergence rate stability problem for nonlinear impulsive stochastic systems (NISSs). To solve the issue, a novel methodology of sliding mode surface design is presented by combining the definition of interval stability with the T-S fuzzy technique. A pioneering class of sliding mode controllers is constructed in accordance with the characteristics of the designed sliding mode surfaces and the sigmoid function. These controllers can intelligently adjust the convergence rate of the system according to practical requirements, thereby addressing the limitation of fixed convergence rate in existing results. Moreover, the proposed controllers can effectively suppress jitter and analyze the effects of different sigmoid functions on jitter suppression. Sufficient conditions are derived to ensure that the states of the NISSs reach the designed surfaces in finite time and to achieve variable convergence rate stability. The excellent performance of the proposed theoretical strategy in achieving adjustable rate convergence of the system is demonstrated through a simulation of the ball-beam system.

Dimensionality Reduction Method for the Output Regulation of Boolean Control Networks

This article proposes a dimensionality reduction approach to study the output regulation problem (ORP) of Boolean control networks (BCNs), which has much lower computational complexity than previous results. First, an auxiliary system which is much smaller in scale than the augmented system in previous approach is constructed. By analyzing the set stabilization of the auxiliary system as well as the original BCN, a necessary and sufficient condition to detect the solvability of the ORP is presented. Second, a method to design the state feedback controls for the ORP is proposed. Finally, two biological examples are given to demonstrate the effectiveness and advantage of the obtained new results.

Sampled-Data Control for Exponential Synchronization of Delayed Inertial Neural Networks With Aperiodic Sampling and State Quantization

This article is devoted to dealing with exponential synchronization for inertial neural networks (INNs) with heterogeneous time-varying delays (HTVDs) under the framework of aperiodic sampling and state quantization. First, by taking the effect of aperiodic sampling and state quantization into consideration, a novel quantized sampled-data (QSD) controller with time-varying control gain is designed to tackle the exponential synchronization of INNs. Second, considering the available information of the lower and upper bounds of each HTVD, a refined Lyapunov-Krasovskii functional (LKF) is proposed. Meanwhile, an improved looped-functional method is utilized to fully capture the characteristic of practical sampling patterns and further relax the positive definiteness requirement for LKF. Consequently, less conservative exponential synchronization conditions with extra flexibility are derived. Finally, a numerical example is employed to demonstrate the effectiveness and advantages of the proposed synchronization method.

Synchronization of Stochastic Neural Networks Using Looped-Lyapunov Functional and Its Application to Secure Communication

This study aims to investigate the synchronization of user-controlled and uncontrolled neural networks (NNs) that exhibit chaotic solutions. The idea behind focusing on synchronization problems is to design the user-desired NNs by emulating the dynamical properties of traditional NNs rather than redefining them. Besides, instead of conventional NNs, this study considers NNs with significant factors such as time-dependent delays and uncertainties in the neural coefficients. In addition, information transmission over transmission may experience stochastic disturbances and network transmission. These factors will result in a stochastic differential NN model. Analyzing the NNs without these factors may be incompatible during the implementation. Theoretically, the model with stochastic disturbances can be considered a stochastic differential model, and the stability conditions are derived by employing Itô's formula and appropriate integral inequalities. To achieve synchronization, the sampled-data-based control scheme is proposed because it is more effective while information is being transmitted over networks. In contrast to the existing studies, this study contributes in terms of handling stochastic disturbances, effects of time-varying delays, and uncertainties in the system parameters via looped-type Lyapunov functional. Besides this, in the application view, delayed NNs are employed as a cryptosystem that helps to secure the transmission between the sender and the receiver, which is explored by illustrating the statistical measures evaluated for the standard images. From the simulation results, the proposed control and derived sufficient conditions can provide better synchronization and the proposed delayed NNs give a better cryptosystem.

Novel criteria of sampled-data synchronization controller design for gated recurrent unit neural networks under mismatched parameters

Synchronization between neural networks (NNs) has been intensively investigated to analyze stability, convergence properties, neuronal behaviors and response to various inputs. However, synchronization techniques of NNs with gated recurrent units (GRUs) have not been provided until now due to their complicated nonlinearity. In this paper, we address the sampled-data synchronization problems of GRUs for the first time, and propose controller design methods using discretely sampled control inputs to synchronize master and slave GRUs. The master and slave GRUs are mathematically modeled as a linear parameter varying (LPV) system in which the parameter of the slave GRUs is constructed independently of the master GRUs. This distinctive modeling feature provides flexibility to extend the existing master and slave NNs into a more general structure. Indeed, the sampled-data synchronization can be achieved by formulating the design condition in terms of linear matrix inequalities (LMIs). The novel sampled-data synchronization criteria are devised by combining the H∞ controller design with the looped-functional approach. The synthesized synchronization controllers guarantee not only asymptotic stability of the synchronization error system with aperiodic sampling, but also provides a satisfactory H∞ control performance. Moreover, the communication efficiency is improved by using the proposed method in which the sampled-data synchronization controller is combined with the event-triggered mechanism. Finally, the numerical example validates the proposed theoretical contributions via simulation results.

Sampled-data exponential consensus of multi-agent systems with Lipschitz nonlinearities

In this paper, the exponential consensus of leaderless and leader-following multi-agent systems with Lipschitz nonlinear dynamics is illustrated with aperiodic sampled-data control using a two-sided loop-based Lyapunov functional (LBLF). Firstly, applying input delay approach to reformulate the resulting sampled-data system as a continuous system with time-varying delay in the control input. A two-sided LBLF which captures the information on sampled-data pattern is constructed and the symmetry of the Laplacian matrix together with Newton-Leibniz formula have been employed to obtain reduced number of decision variables and decreased LMI dimensions for the exponential sampled-data consensus problem. Subsequently, an aperiodic sampled-data controller was designed to simplify and enhance stability conditions for computation and optimization purposes in the proposed approach. Finally, based on the controller design, simulation examples including the power system are proposed to illustrate the theoretical analysis, moreover, a larger sampled-data interval can be acquired by this method than other literature, thereby conserving bandwidth and reducing communication resources.

Synchronization control of time-delay neural networks via event-triggered non-fragile cost-guaranteed control

This paper is devoted to event-triggered non-fragile cost-guaranteed synchronization control for time-delay neural networks. The switched event-triggered mechanism, which combines periodic sampling and continuous event triggering, is used in the feedback channel. A piecewise functional is first applied to fully utilize the information of the state and activation function. By employing the functional, various integral inequalities, and the free-weight matrix technique, a sufficient condition is established for exponential synchronization and cost-related performance. Then, a joint design of the needed non-fragile feedback gain and trigger matrix is derived by decoupling several nonlinear coupling terms. On the foundation of the joint design, an optimization scheme is given to acquire the minimum cost value while ensuring exponential stability of the synchronization-error system. Finally, a numerical example is used to illustrate the applicability of the present design scheme.