Mixed Time Delays Research Articles

Adaptive observer-based projective synchronization for chaotic neural networks with mixed time delays

This paper addresses adaptive projective synchronization of chaotic neural networks with mixed time delays based on an observer-based design strategy. For this, the idea of designing nonlinear state observers is used, and a novel adaptive observer-based controller is given to provide projective synchronization between the master and the slave chaotic systems. Lyapunov theorem is also utilized to obtain the adaptation laws for tuning the controller when the parameters of the master system are unknown. The proposed control scheme is successfully applied for projective synchronization of two chaotic neural networks with mixed delays. The simulation results demonstrate the feasibility and efficiency of the presented method.

State Estimation of Discrete-Time Switched Neural Networks With Multiple Communication Channels.

In this paper, the state estimation problem for a class of discrete-time switched neural networks with modal persistent dwell time (MPDT) switching and mixed time delays is investigated. The considered switching law, not only generalizes the commonly studied dwell-time (DT) and average DT (ADT) switchings, but also further attaches mode-dependency to the persistent DT (PDT) switching that is shown to be more general. Multiple communication channels, which include one primary channel and multiredundant channels, are considered to coexist for the state estimation of underlying switched neural networks. The desired mode-dependent filters are designed such that the resulting filtering error system is exponentially mean-square stable with a guaranteed nonweighted generalized H2 performance index. It is verified that better filtering performance index can be achieved as the number of channels to be used increases. The potential and effectiveness of the developed theoretical results are demonstrated via a numerical example.

Event-triggered H ∞ state estimation for discrete-time neural networks with mixed time delays and sensor saturations

In this paper, the event-triggered H ∞ state estimation problem is investigated for a class of neural networks with mixed time delays and sensor saturations. The mixed time delays consist of discrete and distributed delays. The measurement outputs are subject to the sensor saturations due to the physical constraints. Through the available measurement outputs, the main purpose of the addressed problem is to design a state estimator to estimate the actual neural states. In order to improve the efficiency in resource utilization, an event-triggered mechanism is employed to decide whether the received measurement output is transmitted to the state estimator. Different from the existing event-triggering strategies, the triggering condition is given for each sensor, and the measurement output from each sensor is sent according to their separate triggering conditions. By using the Lyapunov functional approach, sufficient conditions are derived to guarantee that the estimation error dynamics is exponentially stable and the H ∞ performance requirement is satisfied. Then, the desired H ∞ state estimator is designed in terms of the solution to a linear matrix inequality that can be easily solved by the MATLAB toolboxes. Finally, one simulation example is provided to show the effectiveness of the proposed event-triggered estimation scheme.

Periodicity and multi-periodicity of generalized Cohen–Grossberg neural networks via functional differential inclusions

In this paper, we investigate the periodic dynamical behaviors for a class of general Cohen–Grossberg neural networks with discontinuous right-hand sides and mixed time delays involving both time-varying delays and distributed delays. In view of functional differential inclusions theory, we obtain the existence of global solutions. By means of functional differential inclusions theory and fixed-point theorem of multi-valued maps, the existence of one and multiple positive periodic solutions for the neural networks is given. It is worthy to point out that, without assuming the boundedness or under linear growth condition of the discontinuous neuron activation functions, our results on the existence of one and multiple positive periodic solutions will also be valid. We derive some sufficient conditions for the global exponential stability and convergence of the discontinuous neural networks, in terms of non-smooth analysis theory with generalized Lyapunov approach. Finally, we give some numerical examples to show the applicability and effectiveness of our main results.

Global asymptotic stability of piecewise homogeneous Markovian jump BAM neural networks with discrete and distributed time-varying delays

In this paper, the issue of a global asymptotic stability analysis is developed for piecewise homogeneous Markovian jump BAM neural networks with mixed time delays. By establishing the Lyapunov functional, using mode-dependent discrete delay and applying the linear matrix inequality (LMI) method, a novel sufficient condition is obtained to guarantee the stability of the considered system. A numerical example is provided to demonstrate the feasibility and effectiveness of the proposed results.

Fault estimation for discrete-time switched nonlinear systems with discrete and distributed delays

Summary This paper is concerned with the fault estimation for a class of discrete-time switched nonlinear systems with mixed time delays. The fault existing in the system is assumed to be characterized by an external system, which incorporates the fault's prior knowledge to the considered systems. The fault estimator is designed by using the multiple Lyapunov–Krasovskii functional and average dwell-time approach. Sufficient conditions in the form of linear matrix inequalities (LMIs) are developed to ensure the resulting error system is exponentially stable with an optimized disturbance attenuation level. The gain matrices of the estimator can be easily determined by using the standard optimization toolboxes. Finally, numerical examples and simulation results with the help of real-time systems are given to illustrate the effectiveness and advantages of the obtained results. Copyright © 2016 John Wiley & Sons, Ltd.

Passivity analysis of Markov jump BAM neural networks with mode-dependent mixed time-delays via piecewise-constant transition rates

Passivity problem is studied for Markov jump bi-directional associative memory (BAM) neural networks with both mode-dependent mixed time delays and time-varying transition rates. In this paper, we consider both discrete delay and distributed delay which are all switching based on Markov process r(t). Time-varying transition rates are, respectively, discussed under the cases of known transition rates and partly unknown transition rates. The mode-dependent time-varying character of transition rates is supposed to be piecewise-constant. By utilizing LMIs technique and a class of Lyapunov functionals, a switching delay passivity criterion underlying known transition rates is derived, which can be easily checked by the Matlab LMI Tool Box. Furthermore, we extend the result to passivity analysis of Markov jump BAM neural networks with partly unknown transition rates. The results obtained relate on not only switching discrete delays but also switching distributed delays. Finally, a numerical example is given to illustrate the effectiveness of the results.

Mean-square stability analysis of discrete-time stochastic Markov jump recurrent neural networks with mixed delays

In this paper, the problem of mean-square stability analysis for discrete-time stochastic Markov jump recurrent neural networks with time-varying mixed delays is considered. The Markov jumping transition probabilities are assumed completely unknown but piecewise homogeneous, and the mixed time delays under consideration comprise both time-varying discrete delay and infinite distributed delay. In the framework of the delay partitioning approach, the informations of the delay distribution probability are fully considered. With a novel Lyapunov functional, a sufficient delay-dependent condition is established, which is characterized in terms of Linear Matrix Inequalities (LMIs). Finally, a numerical example is given to demonstrate the effectiveness of the obtained results.

Design of exponential state estimators for neutral-type neural networks with mixed time delays

In this paper, the state estimation problem is dealt with for a class of neutral-type neural networks with mixed time delays. We aim at designing a state estimator to estimate the neuron states, through available output measurements, such that the dynamics of the estimation error is globally exponentially stable in the presence of mixed time delays. By using the Lyapunov-Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish sufficient conditions to guarantee the existence of the state estimators. A simulation example is exploited to show the usefulness of the derived LMI-based stability conditions.

Neural Network-Based Passive Filtering for Delayed Neutral-Type Semi-Markovian Jump Systems.

This paper investigates the problem of exponential passive filtering for a class of stochastic neutral-type neural networks with both semi-Markovian jump parameters and mixed time delays. Our aim is to estimate the states by designing a Luenberger-type observer, such that the filter error dynamics are mean-square exponentially stable with an expected decay rate and an attenuation level. Sufficient conditions for the existence of passive filters are obtained, and a convex optimization algorithm for the filter design is given. In addition, a cone complementarity linearization procedure is employed to cast the nonconvex feasibility problem into a sequential minimization problem, which can be readily solved by the existing optimization techniques. Numerical examples are given to demonstrate the effectiveness of the proposed techniques.

Improved Stabilization Criteria for Neutral Time-Delay Systems

This paper addresses the stabilization conditions for neutral systems with mixed time delays. By constructing a novel class of Lyapunov functionals which contains an augmented Lyapunov functional, using a new class of improved Jensen’s like inequalities, two improved delay-dependent stability criteria are firstly established. Next, state feedback controllers are designed according to the stability conditions in different cases. Finally, five numerical examples are provided to demonstrate the theoretical results.

Partial state estimation of LTI systems with multiple constant time-delays

Functional observer design for Multi-Input Multi-Output (MIMO) Linear Time-Invariant (LTI) systems with multiple mixed time delays in the states of the system is addressed. Two structures for the design of a minimum-order observer are considered: 1 – delay-dependent, and 2 – internal-delay independent. The parameters of the delay-dependent observer are designed using the Lyapunov Krasovskii approach. The delay-dependent exponential stability of the observer for a specified convergence rate and delay values is guaranteed upon the feasibility of a set of Linear Matrix Inequalities (LMIs) together with a rank condition. Using the descriptor transformation, a modified Jensen׳s inequality, and improved Park׳s inequality, the results can be less conservative than the available functional observer design methods that address LTI systems with single state delay. Furthermore, the necessary and sufficient conditions of the asymptotic stability of the internal-delay independent observer are obtained, which are shown to be independent of delay. Two illustrative numerical examples and simulation studies confirm the validity and highlight the performance of the proposed theoretical achievements.

Projective synchronization adaptive control for different chaotic neural networks with mixed time delays

Abstract An adaptive control schemes is presented to the projective synchronization of different chaotic neural networks with mixed time delays. The adaptive controller is designed by a linear matrix inequality approach. The proposed approach in this paper gives the flexibility to construct one adaptive control law, and the merit of the adaptive controller with one parameter is that projective synchronization errors can be reached zero field at fast speed. Finally, numerical simulation results are given to validate the design method.

Exponential stability of Markovian jumping Cohen–Grossberg neural networks with mixed mode-dependent time-delays

In this paper, the exponential stability problem is investigated for a class of Cohen–Grossberg neural networks with Markovian jumping parameter and mixed time-delays. The mixed time-delays under consideration consist of both the mode-dependent discrete time-delays and the mode-dependent distributed time-delays. By constructing a new Lyapunov–Krasovskii functional and employing the stochastic analysis techniques, sufficient conditions are proposed to guarantee that the addressed neural networks are exponentially stable in the mean square sense. It is shown that the developed stability criteria can be easily verified by using the standard numerical software. Finally, an illustrative example is provided to show the feasibility and usefulness of the developed results.

Lag synchronization for Cohen–Grossberg neural networks with mixed time-delays via periodically intermittent control

ABSTRACTIn this paper, the exponential lag synchronization for a class of Cohen–Grossberg neural networks with discrete time-delays and distributed delays is investigated via periodically intermittent control. Some simple and useful criteria are derived by using mathematical induction method and the analysis technique which are different from the methods employed in correspondingly previous works. Finally, two examples and their numerical simulations are given to demonstrate the effectiveness of the proposed control schemes.

Synchronization for distributed parameter NNs with mixed delays via sampled-data control

A sampled-data synchronization scheme is developed for a class of distributed parameter neural networks with mixed time delays. The design approach of the desired sampled data controller is also presented. We propose a sampled-data controller design, in which the sampled-data (in time) measurements of the state are taken in a finite number of fixed sampling points in the spatial domain. It is supposed that the sampling intervals in time and in space are bounded. Based on the extended Wirtinger’s inequality, an appropriate Lyapunov–Krasovskii functional and some free-weighting matrices are used to establish simple and less conservative synchronization criteria, which can ensure that the master systems synchronize with the slave systems via direct Lyapunov approach in terms of linear matrix inequalities. Finally, numerical simulations are carried out to demonstrate the effectiveness of the proposed synchronization method.

Sampled-data synchronization of randomly coupled reaction–diffusion neural networks with Markovian jumping and mixed delays using multiple integral approach

This paper is devoted to investigate the problem of global asymptotic synchronization of an array of N randomly coupled reaction---diffusion neural networks with Markovian jumping parameters and mixed delays using sampled-data control technique. The jump parameters are determined by a continuous-time, discrete-state Markovian chain, and the mixed time delays under consideration comprise both discrete and distributed delays. A multiple integral inequality is proposed firstly in Markovian jump reaction---diffusion neural networks with mixed delays. Through constructing appropriate Lyapunov---Krasovskii functional including multiple integral terms, some novel synchronization criteria in terms of linear matrix inequalities are derived. The obtained LMIs can be easily verified for feasibility through any of the available softwares. Finally, numerical examples with simulations are provided to illustrate the effectiveness of the proposed theoretical results.

An Event-Triggered Approach to State Estimation for a Class of Complex Networks With Mixed Time Delays and Nonlinearities.

In this paper, the state estimation problem is investigated for a class of discrete-time complex networks subject to nonlinearities, mixed delays, and stochastic noises. A set of event-based state estimators is constructed so as to reduce unnecessary data transmissions in the communication channel. Compared with the traditional state estimator whose measurement signal is received under a periodic clock-driven rule, the event-based estimator only updates the measurement information from the sensors when the prespecified "event" is violated. Attention is focused on the analysis and design problem of the event-based estimators for the addressed discrete-time complex networks such that the estimation error is exponentially bounded in mean square. A combination of the stochastic analysis approach and Lyapunov theory is employed to obtain sufficient conditions for ensuring the existence of the desired estimators and the upper bound of the estimation error is also derived. By using the convex optimization technique, the gain parameters of the desired estimators are provided in an explicit form. Finally, a simulation example is used to demonstrate the effectiveness of the proposed estimation strategy.

Passivity analysis of spatially and temporally BAM neural networks with the Neumann boundary conditions

In the paper, a delay-differential equation modeling a bidirectional associative memory neural networks (BAM NNs) with reaction-diffusion terms is investigated, for which the input and output variables are varied with the time and space variables. By taking advantage of the inequality techniques, some Lyapunov-Krasovskii functional candidates are introduced to arrive at the novel sufficient conditions that warrant the passivity of spatially and temporally BAM NNs with mixed time delays. Moreover, when the parameter uncertainties appear in spatially and temporally BAM NNs, the criterion for robust passivity is also given. Novel passivity criteria are proposed in terms of inequalities, which can be checked easily. A numerical example is provided to demonstrate the effectiveness of the proposed results.

$$H_{\infty }$$ H ∞ filtering for discrete-time fuzzy stochastic neural networks with mixed time-delays

The $$H_{\infty }$$ filter problem for a class of fuzzy stochastic discrete neural networks system with mixed delays is studied in this paper. The mixed delays consist of discrete and distributed delays. Based on discrete inequality technic and the Lyapunov–Krasovskii functional approach, sufficient conditions for the existence of admissible filters are established in terms of linear matrix inequalities, which ensure the asymptotical mean-square stability as well as a prescribed $$H_{\infty }$$ disturbance attenuation level. Examples and simulations are provided to illustrate the effectiveness of the proposed method.