Finite/fixed-time synchronization control of coupled memristive neural networks

Finite-time and fixed-time synchronization (FAFS) of coupled memristive neural networks (CMNNs) with discontinuous feedback functions are explored in this paper. Firstly, a more comprehensive stability theory is systematically established. Secondly, by designing adaptive feedback controller and discontinuous feedback controller, both finite-time and fixed-time synchronization can be realized through regulating the main control parameter. Thirdly, 1-norm and quadratic-norm Lyapunov functions are considered simultaneously in this article, while in estimating the settling time, the former one is more accurate than the latter one under the same synchronization criteria. Finally, in numerical simulation, the analysis and comparison of the proposed controllers are given to show the effectiveness of the corresponding results.     

Lag synchronization for fractional-order memristive neural networks with time delay via switching jumps mismatch

This paper studies drive-response synchronization in fractional-order memristive neural networks (FMNNs) with switching jumps mismatch. A comparison theorem for fractional-order systems with variable order is provided first. Theories of fractional order Filippov differential inclusions are used to treat FMNNs because the parameters of FMNNs are state dependent and the FMNNs has discontinuous right hand sides. Based on Laplace transform and linear feedback control, some lag quasi-synchronization conditions are obtained with variable order α: 0?<?α?<?1 and 1?<?α?<?2. The error level is estimated and the larger synchronization regain is discussed. Finally, two numerical examples are presented to illustrate the effectiveness of our proposed theorems.     

Novel discontinuous control for exponential synchronization of memristive recurrent neural networks with heterogeneous time-varying delays

This paper investigates the exponential synchronization problem of memristive recurrent neural networks (MRNNs) with heterogeneous time-varying delays (HTVDs). First, a novel discontinuous feedback control is designed, in which a tunable scalar is introduced. The tunable scalar makes the controller more flexible in reducing the upper bound of the control gain. Based on this control scheme, the double integral term can be successfully used to construct the LKF. Second, New method for tackling memristive synaptic weights and new estimation technique are presented. Third, based on the LKF and estimation technique, synchronization criterion is derived. In comparison with existing results, the established criterion is less conservatism thanks to the double integral term of the LKF. Finally, numerical simulations are presented to validate the effectiveness and advantages of the proposed results.     

Decentralized adaptive synchronization with bounded identification errors for discrete-time nonlinear multi-agent systems with unknown parameters and unknown high-frequency gains

This paper addresses the challenging problem of decentralized adaptive control for a class of coupled hidden leader-follower multi-agent systems, in which each agent is described by a nonlinearly parameterized uncertain model in discrete time and can interact with its neighbors via the history information from its neighbors. One of the agents is a leader, who knows the desired reference trajectory, while other agents cannot receive the desired reference signal or are unaware of existence of the leader. In order to tackle unknown internal parameters and unknown high-frequency gains, a projection-type parameter estimation algorithm is proposed. Based on the certainty equivalence principle and neighborhood history information, the decentralized adaptive control is designed, under which, the boundedness of identification error is guaranteed with the help of the Lyapunov theory. Under some conditions, it is shown that the multi-agent system eventually achieves synchronization in the presence of strong couplings. Finally, a simulation example is given to support the results of the proposed scheme.     

A class of fast fixed-time synchronization control for the delayed neural network

This paper deals with the synchronization control of a class of delayed neural networks using a fast fixed-time control theory. By employing Lyapunov stability theory, a novel sufficient criterion is derived such that two neural networks can be synchronized within a fixed-time. Compared with some existing results, the proposed controller can render two neural networks faster synchronized. A numerical example is given to demonstrate the effectiveness of the criterion.     

Mode-dependent stochastic synchronization criteria for Markovian hybrid neural networks with random coupling strengths

This paper is concerned with the stochastic synchronization problem for a class of Markovian hybrid neural networks with random coupling strengths and mode-dependent mixed time-delays in the mean square. First, a novel inequality is established which is a double integral form of the Wirtinger-based integral inequality. Next, by employing a novel augmented Lyapunov–Krasovskii functional (LKF) with several mode-dependent matrices, applying the theory of Kronecker product of matrices, Barbalat’s Lemma and the auxiliary function-based integral inequalities, several novel delay-dependent conditions are established to achieve the globally stochastic synchronization for the mode-dependent Markovian hybrid coupled neural networks. Finally, a numerical example with simulation is provided to illustrate the effectiveness of the presented criteria.     

Finite-time synchronization of delayed dynamical networks via aperiodically intermittent control

In this paper, we concern the finite-time synchronization problem for delayed dynamical networks via aperiodically intermittent control. Compared with some correspondingly previous results, the intermittent control can be aperiodic which is more general. Moreover, by establishing a new differential inequality and constructing Lyapunov function, several useful criteria are derived analytically to realize finite-time synchronization for delay complex networks. Additionally, as a special case, some sufficient conditions ensuring the finite-time synchronization for a class of coupled neural network are obtained. It is worth noting that the convergence time is carefully discussed and does not depend on control widths or rest widths for the proposed aperiodically intermittent control. Finally, a numerical example is given to demonstrate the validness of the proposed scheme.     

Asymptotic stability of delayed fractional-order fuzzy neural networks with impulse effects

In this paper, we investigate the asymptotic stability of fractional-order fuzzy neural networks with fixed-time impulse and time delay. According to the fractional Barbalat’s lemma, Riemann–Liouville operator and Lyapunov stability theorem, some sufficient conditions are obtained to ensure the asymptotic stability of the fractional-order fuzzy neural networks. Two numerical examples are also given to illustrate the feasibility and effectiveness of the obtained results.     

Finite-time synchronization of delayed complex dynamic networks via aperiodically intermittent control

In this paper, the finite-time synchronization problem of complex dynamic networks with time delay is studied via aperiodically intermittent control. By compared with the existed results concerning aperiodically intermittent control, some new results are obtained to guarantee the synchronization of networks in a finite time. Especially, a new lemma is proposed to reduce the convergence time. In addition, based on aperiodically intermittent control scheme, the essential condition ensuring finite-time synchronization of dynamic networks is also obtained, and the convergence time is closely related to the topological structure of networks and the maximum ratio of the rest width to the aperiodic time span. Finally, a numerical example is provided to verify the validness of the proposed theoretical results.     

Non-fragile exponential synchronization of delayed complex dynamical networks with transmission delay via sampled-data control

This paper is devoted to the non-fragile exponential synchronization problem of complex dynamical networks with time-varying coupling delays via sampled-data static output-feedback controller involving a constant signal transmission delay. The dynamics of the nodes contain s quadratically restricted nonlinearities, and the feedback gain is allowed to have norm-bounded time-varying uncertainty. The control design is based on a Lyapunov–Krasovskii functional, which consists of the sum of terms assigned to the individual nodes, i.e., it is constructed without merging the complex dynamical network’s nodes into a single large-scale system. In this way, the proposed design method has substantially reduced computational complexity and improved conservativeness, and guaranties non-fragile exponential stability of the error system. The sufficient stability condition is expressed in terms of linear matrix inequalities that are solvable by standard tools. The efficiency of the proposed method is illustrated by numerical examples.     

Input-to-state stability of impulsive inertial memristive neural networks with time-varying delayed

The property of input-to-state stability (ISS) of inertial memristor-based neural networks with impulsive effects is studied. Firstly, according to the characteristics of memristor and inertial neural networks, the inertial memristor-based neural networks are built. Secondly, based on the impulsive control theory, the average impulsive interval approach, Halanay differential inequality, Lyapunov method and comparison property, some sufficient conditions ensuring ISS of the inertial memristor-based neural networks under impulsive controller are derived. In this paper, we consider two types of impulse, stabilizing impulses and destabilizing impulses. When the inertial memristor-based neural networks are originally not ISS, by choosing a suitable lower bound of the average impulsive interval, the stabilizing impulses can be used to stabilize the inertial memristor-based neural networks. On the contrary, the inertial memristor-based neural networks are originally ISS, by restricting the upper bound of the average impulsive interval, the ISS of inertial memristor-based neural networks with destabilizing impulses can be ensured. Finally, numerical results are presented to illustrate the main results.     

Robust exponential stability of uncertain impulsive stochastic neural networks with delayed impulses

In this paper, by using Lyapunov functions, Razumikhin techniques and stochastic analysis approaches, the robust exponential stability of a class of uncertain impulsive stochastic neural networks with delayed impulses is investigated. The obtained results show that delayed impulses can make contribution to the stability of system. Compared with existing results on related problems, this work improves and complements ones from some works. Two examples are discussed to illustrate the effectiveness and the advantages of the results obtained.     

Extended dissipative learning of time-delay recurrent neural networks

The paper addresses the issue of extended dissipative learning for a class of delayed recurrent neural networks. Both time-varying delay and time-invariant delay are taken into account. By choosing appropriate Lyapunov–Krasovkii functionals and utilizing some inequalities, several weight learning rules are developed for ensuring the network to be asymptotically stable and extended dissipative. The existence conditions for these learning strategies consist of a few linear matrix inequalities, which are able to be verified readily by Matlab software. Two numerical examples are employed to show the effectiveness and low conservatism of the proposed learning rules.     

Adaptive synchronization of unknown heterogeneous agents: An adaptive virtual model reference approach

This work deals with state synchronization of heterogeneous linear agents with unknown dynamics. The problem is solved by formulating the synchronization problem as a special model reference adaptive control where each agent tries to converge to the model defined by its neighbors. For those agents that do not know the reference signal that drives the flock, a fictitious reference is estimated in place of the actual one: the estimation of such reference is distributed and requires measurements from neighbors. By using a matching condition assumption, which is imposed so that the agents can converge to the same behavior, the fictitious reference estimation leads to adaptive laws for the feedback and the coupling gains arising from distributed matching conditions. In addition, the coupling connection is not scalar as in most literature, but possibly vector-valued. The proposed approach is applicable to heterogeneous agents with arbitrarily large matched uncertainties. A Lyapunov-based approach is derived to show analytically asymptotic convergence of the synchronization error: robustification in the presence of bounded errors or unknown (constant) leader input is also discussed. Finally, a motivational example is presented in the context of Cooperative Adaptive Cruise Control and numerical examples are provided to demonstrate the effectiveness of the proposed method.     

Fixed-time outer synchronization of hybrid-coupled delayed complex networks via periodically semi-intermittent control

In this paper, the fixed-time synchronization between two delayed complex networks with hybrid couplings is investigated. The internal delay, transmission coupling delay and self-feedback coupling delay are all included in the network model. By introducing and proving a new and important differential equality, and utilizing periodically semi-intermittent control, some fixed-time synchronization criteria are derived in which the settling time function is bounded for any initial values. It is shown that the control rate, network size and node dimension heavily influence the estimating for the upper bound of the convergence time of synchronization state. Finally, numerical simulations are performed to show the feasibility and effectiveness of the control methodology by comparing with the corresponding finite-time synchronization problem.     

Nonlinear model-predictive control with disturbance rejection property using adaptive neural networks

In this paper, a method is proposed to reject disturbances in the model predictive control (MPC) strategy. In addition, uncertainties in the system parameters (i.e., internal disturbances) are considered as well. To achieve these goals, adaptive neural networks are designed as the predictor model and as the nonlinear disturbance observer, respectively. The disturbances are rejected via the optimization problem of the MPC. Stability of the closed-loop system is studied based on the Input-to-State Stability method. The proposed method is applied to the pH neutralization process and CSTR system and its effectiveness in optimal rejection of the disturbances and satisfying the system constrains is compared with the feed-forward control method.     

Exponential synchronization of coupled neutral-type neural networks with mixed delays via quantized output control

In this paper, new control scheme is considered for exponential synchronization of coupled neutral-type neural networks (NTNNs) with both bounded discrete-time delay and unbounded distributed delay (mixed delays). It is assumed that only the measured output can be utilized to design the controller. Quantized output controllers (QOCs) are considered to save the bits rate of communication channels and the bandwidth. The main difficulty in solving this problem is to cope with the neutral terms, the delays, and the uncertainties induced by the quantization simultaneously. By designing new Lyapunov–Krasovskii functionals and proposing novel analytical techniques, sufficient conditions are derived to ensure the exponential synchronization of the interested NTNNs. The control gains are given by solving a set of linear matrix inequalities (LMIs), which are not necessarily to be negative-definite matrices. Numerical examples are provided to verify the effectiveness and merits of the proposed approach.     

Projective synchronization in fixed time for complex dynamical networks with nonidentical nodes via second-order sliding mode control strategy

This paper is concerned with the global projective synchronization in fixed time for complex dynamical networks (CDNs) with nonidentical nodes in the presence of disturbances. Firstly, in order to realize the fixed-time projective synchronization of CDNs with matched disturbances, the second-order sliding mode is established, and the global fixed-time reachability of sliding manifolds is analyzed. The fixed-time stability of the sliding mode dynamics is also proved analytically based on Lyapunov stability theory. Moreover, the fixed convergence time of both reaching and sliding mode phases can be adjusted to any desired values in advance by the choice of the designable parameters. Secondly, in order to realize the fixed-time projective synchronization of CDNs with mismatched disturbances, a super-twisting-like (STL) controller, which does not require the information of the derivative of the sliding variable, is designed, and the synchronization condition is addressed in terms of linear matrix inequalities (LMIs). By the proposed controllers, continuous control signals can be provided to reduce the chattering effect and improve the control accuracy. Finally, two numerical examples are given to demonstrate the validity of the theoretical results and the the feasibility of the proposed approaches.     

Stability of delayed Hopfield neural networks under a sublinear expectation framework

In this paper, we consider the stability of a class of stochastic delay Hopfield neural networks driven by G-Brownian motion. Under a sublinear expectation framework, we give the definition of exponential stability in mean square and construct some conditions such that the stochastic system is exponentially stable in mean square. Moreover, we also consider the stability of the Euler numerical solution of such equation. Finally, we give an example and its numerical simulation to illustrate our results.     

Distributed MPC-based adaptive control for linear systems with unknown parameters

This paper is concerned with the adaptive control problem for a class of linear discrete-time systems with unknown parameters based on the distributed model predictive control (MPC) method. Instead of using the system state, the state estimate is employed to model the distributed state estimation system. In this way, the system state does not have to be measurable. Furthermore, in order to improve the system performance, both the output error and its estimation are considered. Moreover, a novel Lyapunov functional, comprised of a series of distributed traces of estimation errors and their transposes, has been presented. Then, sufficient conditions are obtained to guarantee the exponential ultimate boundedness of the system as well as the asymptotic stability of the error system by solving a nonlinear programming (NP) problem subject to input constraints. Finally, the simulation examples is given to illustrate the effectiveness and the validity of the proposed technique.