Non-reduced Order Research Articles

Passivity and robust passivity of inertial memristive neural networks with time-varying delays via non-reduced order method.

This study examines the concepts of passivity and robust passivity in inertial memristive neural networks (IMNNs) that feature time-varying delays. By using non-smooth analysis and the passivity theorem, algebraic criteria for both passivity and robust passivity are derived by using the non-reduced order method. The proposed criteria, based on the non-reduced order method, effectively reduce the complexity of derivation and computation, thereby simplifying the verification process. Furthermore, asymptotic stability criteria for IMNNs are established in relation to the passivity conditions. In conclusion, two numerical examples are provided to confirm the theoretical results.

Finite-time synchronization for a fully complex-valued BAM inertial neural network with proportional delays via non-reduced order and non-separation approach

This paper focuses on finite-time synchronization (FinTS) for fully complex-valued bidirectional associative memory inertial neural networks (FCV-BAM-INNs) with proportional delays via non-reduced order and non-separation approach. Firstly, a model of the FCV-BAM-INNs with proportional delays is established. Secondly, by using the non-reduced order transformation method of inertial neural networks (INNs) and the non-separation method of complex-valued neural networks (CVNNs), an adjustable complex feedback control law with memory is designed to reach the FinTS of the drive–response FCV-BAM-INNs with proportional delays. Thirdly, some new delay-independent algebraic sufficient criteria are formed to guarantee FinTS of FCV-BAM-INNs with proportional delays by applying non smooth theory and inequalities in the complex domain, which are flexible and adjustable and easy to implement in applications. Moreover, the settling time of FinTS theoretically is calculated. Finally, some numerical simulations and an application on image encryption and decryption as evidences of the validity and availability of the results.

Event-triggered-based fixed/preassigned-time synchronization control of second-order neural networks with distributed delays

In this article, a kind of second-order neural networks with variable coefficients and distributed delays are discussed. At first, new lemmas about fixed/preassigned-time synchronization for such system are respectively constructed. Then, some novel criteria are given to get fixed/preassigned-time synchronization for such delayed system based on the these lemmas. Unlike feedback controllers are used in previous works, two effective event-triggered controllers are, respectively, proposed here to investigate the second-order neural networks. In addition, event-triggered control and non-reduced order way are combined use to realize fixed/preassigned-time synchronization for such delayed system at the first time, which has advantages from both efficiency of control and brevity of criterion. Finally, two examples are presented to show validity of the proposed criteria.

Finite-Time Stabilization of Inertial Memristive Neural Networks via Nonreduced Order Method.

This article investigates the finite-time stabilization problem of inertial memristive neural networks (IMNNs) with bounded and unbounded time-varying delays, respectively. To simplify the theoretical derivation, the nonreduced order method is utilized for constructing appropriate comparison functions and designing a discontinuous state feedback controller. Then, based on the controller, the state of IMNNs can directly converge to 0 in finite time. Several criteria for finite-time stabilization of IMNNs are obtained and the setting time is estimated. Compared with previous studies, the requirement of differentiability of time delay is eliminated. Finally, numerical examples illustrate the usefulness of the analysis results in this article.

Scaled consensus of second-order nonlinear multi-agent systems with fully distributed adaptive aperiodically intermittent communication: A non-reduced order approach

Scaled consensus of second-order nonlinear multi-agent systems with fully distributed adaptive aperiodically intermittent communication: A non-reduced order approach

Projective Synchronization of Inertial Quaternion-Valued Neural Networks via Non-reduced Order Approach

In this article, the issue on projective synchronization of delayed inertial quaternion-valued neural networks (IQVNNs) is investigated. Different from most existing literature, we adopt the non-reduced order approach to deal with IQVNNs described by second order differential equations. By introducing a novel Lyapunov functional, several sufficient criteria are presented in component form to ensure the projective synchronization between master–slave systems. A numerical experiment demonstrates the feasibility of control strategy as well as the correctness of theoretical results.

Passivity and robust passivity of impulsive inertial neural networks with proportional delays under the non-reduced order approach

This paper primarily addresses the problems of passivity and robust passivity of impulsive inertial neural networks (IINNs) with proportional delays. By constructing the Lyapunov functional directly on the original system using the non-reduced order approach, some passivity and robust passivity criteria for IINNs are addressed. In comparison with the order reduction method utilized in the existing articles, the non-reduced order method is more in line with real requirements and can better analyze the dynamic behavior of inertial neural networks (INNs). Meanwhile, the results in this paper are all in algebraic form, which are easy to verify. To demonstrate the effectiveness of the results derived, numerical examples are presented at the end.

Non-Reduced Order Method to Parameterized Sampled-Data Stabilization of Inertial Neural Networks With Actuator Saturation

Non-Reduced Order Method to Parameterized Sampled-Data Stabilization of Inertial Neural Networks With Actuator Saturation

Influences of time delay and connection topology on a multi-delay inertial neural system.

Multiple delays and connection topology are the key parameters for the realistic modeling of networks. This paper discusses the influences of time delays and connection weight on multi-delay artificial neural models with inertial couplings. Firstly, sufficient conditions of some singularities involving static bifurcation, Hopf bifurcation, and pitchfork-Hopf bifurcation are presented by analyzing the transcendental characteristic equation. Secondly, taking self-connection weight and coupling delays as adjusting parameters and utilizing the parameter perturbation with the aid of the non-reduced order technique for the first time, rich dynamics near zero-Hopf interaction are obtained on the plane with self-connected weight and coupling delay as abscissa and ordinate. The multi-delay inertial neural system can exhibit coexisting attractors such as a pair of nontrivial equilibrium points and a periodic orbit with nontrivial equilibrium points. Self-connected weight can affect the number and dynamics of the system equilibrium points, while time delays can contribute to both trivial equilibrium and non-trivial equilibrium losing their stability and generating limit cycles. Simulation plots are displayed with computer software to support the established main results. Compared with the traditional reduced-order method, the used method here is simple and valid with less computation. The key research findings of this paper have significant theoretical guiding value in dominating and optimizing networks.

Scaled consensus of second-order nonlinear multi-agent systems with distributed adaptive control via non-reduced order method

In this article, the leaderless and leader-following scaled consensus (SC) of second-order multi-agent systems (SOMASs) with nonlinear dynamics under distributed adaptive control are investigated by non-reduced order method (NROM). Firstly, the NROM is first applied to transform the variable-replaced SOMASs into a pure second-order differential system. Secondly, a novel Lyapunov function involving the error variables and derivative of the error variables is constructed to directly discuss the second-order differential system, which is completely different from the traditional analysis method. Thirdly, two different coupling gains are designed in the light of the position and velocity of the agent to solve the leader-following SC more flexibly. Finally, two numerical examples are cited to verify the practicability of the theoretical derivation.

Event-Triggered Synchronization for Delayed Quaternion-Valued Inertial Fuzzy Neural Networks via Nonreduced Order Approach

This paper mainly studies the synchronization problem for a class of Takagi-Sugeno (T-S) fuzzy quaternion-valued inertial neural networks with time-varying delay through event-triggered control (ETC) scheme. Firstly, a class of quaternion-valued inertial fuzzy neural networks (QVIFNNs) model with time-varying delay is proposed. To avoid the increase of the number of state variables caused by reduced-order method, non-reduced order approach is utilized fully, and a fuzzy exponential gain event-triggered controller is designed so as to occupy the less communication resources. Then, by establishing a novel Lyapunov functional well handling the high-order term, a new synchronization condition is derived under static event-triggered scheme. And then, to further reduce the number of triggers, a dynamic event-triggered condition is developed and the corresponding sufficient criterion is given. Meanwhile, it is proved that the lower bound of event intervals are non-zero positive and the Zeno phenomenons do not exist via rigorous mathematical derivation. Finally, a numerical example is offered to show the effectiveness of the proposed method. A application example for the considered QVIFNNs with time-varying delay is given.

Cluster synchronization for directed coupled inertial reaction-diffusion neural networks with nonidentical nodes via non-reduced order method

The cluster synchronization issues are investigated for directed coupled inertial reaction-diffusion neural networks (CIRDNNs) with nonidentical nodes by imposing two effective pinning control. A novel Lyapunov-Krasovskii functional (LKF) is established to directly analyze the dynamic behavior of CIRDNNs and deal with reaction-diffusion term, inertia term and coupling term. Moreover, based on different desired cluster synchronization states including a set of un-decoupled trajectories and the particular solutions of the decoupled node systems, two class of synchronization criteria in view of algebraic inequalities are derived under two different communication topologies, respectively. Finally, two typical examples are given to verify the theoretical results.

New Results on Finite-Time Synchronization Control of Chaotic Memristor-Based Inertial Neural Networks with Time-Varying Delays

In this work, we are concerned with the finite-time synchronization (FTS) control issue of the drive and response delayed memristor-based inertial neural networks (MINNs). Firstly, a novel finite-time stability lemma is developed, which is different from the existing finite-time stability criteria and extends the previous results. Secondly, by constructing an appropriate Lyapunov function, designing effective delay-dependent feedback controllers and combining the finite-time control theory with a new non-reduced order method (NROD), several novel theoretical criteria to ensure the FTS for the studied MINNs are provided. In addition, the obtained theoretical results are established in a more general framework than the previous works and widen the application scope. Lastly, we illustrate the practicality and validity of the theoretical results via some numerical examples.

Analysis of Hopf–Hopf Interactions Induced by Multiple Delays for Inertial Hopfield Neural Models

The investigation of dynamic behaviors of inertial neural networks depicted by second-order delayed differential equations has received considerable attention. Substantial research has been performed on the transformed first-order differential equations using traditional variable substitution. However, there are few studies on bifurcation dynamics using direct analysis. In this paper, a multi-delay Hopfield neural system with inertial couplings is considered. The perturbation scheme and non-reduced order technique are firstly combined into studying multi-delay induced Hopf–Hopf singularity. This combination avoids tedious computation and overcomes the disadvantages of the traditional variable-substitution reduced-order method. In the neighbor of Hopf–Hopf interaction points, interesting dynamics are found on the plane of self-connected delay and coupled delay. Multiple delays can induce the switching of stable periodic oscillation and periodic coexistence. The explicit expressions of periodic solutions are obtained. The validity of theoretical results is shown through consistency with numerical simulations.

Finite-Time Stabilization Criteria of Delayed Inertial Neural Networks with Settling-Time Estimation Protocol and Reliable Control Mechanism

This work investigates the finite-time stability (FTS) issue for a class of inertial neural networks (INNs) with mixed-state time-varying delays, proposing a novel analytical approach. Firstly, we establish a novel FTS lemma, which is entirely different from the existing FTS theorems, and extend the current research results. Secondly, an improved discontinuous reliable control mechanism is developed, which is more valid and widens the application scope compared to previous results. Then, by using a novel non-reduced order approach (NROA) and the Lyapunov functional theory, novel sufficient criteria are established using FTS theorems to estimate the settling time with respect to a finite-time stabilization of INNs. Finally, the simulation results are given to validate the usefulness of the theoretical results.

New results on fixed/predefined-time synchronization of delayed fuzzy inertial discontinuous neural networks: Non-reduced order approach

This paper focuses on the fixed/predefined-time synchronization control of drive-response fuzzy inertial discontinuous neural networks(FIDNNs) with distributed delays. By using non-smooth analysis, fixed/predefined-time stability lemmas and designing two new fixed/predefined-time feedback controllers, several novel results are given to get fixed-time synchronization(FTS) and predefined-time synchronization(PTS) for the proposed FIDNNs. The fixed/predefined-time results of this paper are derived directly from FIDNNs themselves without variables substitution method. Up until now, very few results are reported on non-reduced order approach to achieve FTS and PTS of FIDNNs with distributed delays. Finally, some simulations and applications are, respectively, carried out to expound the efficacy of the obtained new FTS and PTS criteria.

Exponential Synchronization of Inertial Complex-Valued Fuzzy Cellular Neural Networks with Time-Varying Delays via Periodically Intermittent Control

This paper mainly studies the exponential synchronization issue for the inertial complex-valued fuzzy cellular neural networks (ICVFCNNs) with time-varying delays via periodically intermittent control. To achieve exponential synchronization, we use a non-reduced order and non-separation approach, which is a supplement and innovation to the previous method. Based on directly constructing Lyapunov functional and a novel periodically intermittent control scheme, sufficient conditions for achieving the exponential synchronization of the ICVFCNNs are established. Finally, an example is given to illustrate the validity of the obtained results.

State estimation of quaternion-valued inertial neural networks: non-reduced order method.

This paper concentrates on the problem of state estimation for quaternion-valued inertial neural networks (QVINNs) with nonidentical time-varying delay. Without reducing the original second order system into two first order systems, a non-reduced order method is developed to investigate the addressed QVINNs, which is different from the majority of existing references. By constructing a new Lyapunov functional with tuning parameters, some easily checked algebraic criteria are established to ascertain the asymptotic stability of error-state system with the desired performance. Moreover, an effective algorithm is provided to design the estimator parameters. Finally, a numerical example is given out to illustrate the feasibility of the designed state estimator.

Formula omitted] state estimation of the high-order inertial neural network with time-varying delay: Non-reduced order strategy

As a first attempt, the L2-L∞ state estimation issue of the high-order inertial neural networks with time-varying delay is put forward in this paper. A more direct method, non-reduced order method, is adopted here rather than reducing the order of the original second-order dynamics via substitution of variables. Our main objective is to construct an appropriate state estimator, which can not only guarantee the global h-stability of the undisturbed error dynamics, but also ensure the peak value of the estimation error is kept within a certain range. Through utilizing Lyapunov theory and some simple matrix calculation, a delay-dependent criterion is presented to elaborate the state estimator conforms to the expectation. In the end, an illustrative simulation example shows the correctness of the estimation technique proposed in this paper.

Passivity-based Bipartite Synchronization of Coupled Delayed Inertial Neural Networks via Non-reduced Order Method

Passivity-based Bipartite Synchronization of Coupled Delayed Inertial Neural Networks via Non-reduced Order Method