Mixed Delays Research Articles

Piecewise pseudo almost periodic solutions of interval general BAM neural networks with mixed time-varying delays and impulsive perturbations

<abstract><p>This paper is concerned with piecewise pseudo almost periodic solutions of a class of interval general BAM neural networks with mixed time-varying delays and impulsive perturbations. By adopting the exponential dichotomy of linear differential equations and the fixed point theory of contraction mapping. The sufficient conditions for the existence of piecewise pseudo almost periodic solutions of the interval general BAM neural networks with mixed time-varying delays and impulsive perturbations are obtained. By adopting differential inequality techniques and mathematical methods of induction, the global exponential stability for the piecewise pseudo almost periodic solutions of the interval general BAM neural networks with mixed time-varying delays and impulsive perturbations is discussed. An example is given to illustrate the effectiveness of the results obtained in the paper.</p></abstract>

Almost periodic dynamical behaviors of neutral-type neural networks with discontinuous activations and mixed delays

This paper presents a class of neutral-type neural networks with discontinuous activations and mixed delays. By using differential inclusions theory, the non-smooth analysis theory with Lyapunovlike approach, some new sufficient criteria are given to ascertain the existence, uniqueness and globally exponential stability of the almost periodic solution for the addressed neural network system. Some recent results in the literature are generalized and improved. Finally, simulation results of two topical numerical examples are also delineated to demonstrate the effectiveness of our theoretical results.

Finite-time decentralized event-triggered feedback control for generalized neural networks with mixed interval time-varying delays and cyber-attacks

<abstract><p>This article investigates the finite-time decentralized event-triggered feedback control problem for generalized neural networks (GNNs) with mixed interval time-varying delays and cyber-attacks. A decentralized event-triggered method reduces the network transmission load and decides whether sensor measurements should be sent out. The cyber-attacks that occur at random are described employing Bernoulli distributed variables. By the Lyapunov-Krasovskii stability theory, we apply an integral inequality with an exponential function to estimate the derivative of the Lyapunov-Krasovskii functionals (LKFs). We present new sufficient conditions in the form of linear matrix inequalities. The main objective of this research is to investigate the stochastic finite-time boundedness of GNNs with mixed interval time-varying delays and cyber-attacks by providing a decentralized event-triggered method and feedback controller. Finally, a numerical example is constructed to demonstrate the effectiveness and advantages of the provided control scheme.</p></abstract>

New delay-range-dependent exponential stability criterion and $ H_\infty $ performance for neutral-type nonlinear system with mixed time-varying delays

<abstract><p>For a neutral system with mixed discrete, neutral and distributed interval time-varying delays and nonlinear uncertainties, the problem of exponential stability is investigated in this paper based on the $ H_\infty $ performance condition. The uncertainties are nonlinear time-varying parameter perturbations. By introducing a decomposition matrix technique, using Jensen's integral inequality, Peng-Park's integral inequality, Leibniz-Newton formula and Wirtinger-based integral inequality, utilization of a zero equation and the appropriate Lyapunov-Krasovskii functional, new delay-range-dependent sufficient conditions for the $ H_\infty $ performance with exponential stability of the system are presented in terms of linear matrix inequalities. Moreover, we present numerical examples that demonstrate exponential stability of the neutral system with mixed time-varying delays, and nonlinear uncertainties to show the advantages of our method.</p></abstract>

A sufficient maximum principle for backward stochastic systems with mixed delays.

In this paper, we study the problem of optimal control of backward stochastic differential equations with three delays (discrete delay, moving-average delay and noisy memory). We establish the sufficient optimality condition for the stochastic system. We introduce two kinds of time-advanced stochastic differential equations as the adjoint equations, which involve the partial derivatives of the function $ f $ and its Malliavin derivatives. We also show that these two kinds of adjoint equations are equivalent. Finally, as applications, we discuss a linear-quadratic backward stochastic system and give an explicit optimal control. In particular, the stochastic differential equations with time delay are simulated by means of discretization techniques, and the effect of time delay on the optimal control result is explained.

Adaptive Fixed-Time Synchronization of Delayed Memristor-Based Neural Networks with Discontinuous Activations

Fixed-time synchronization (FTS) of delayed memristor-based neural networks (MNNs) with discontinuous activations is studied in this paper. Both continuous and discontinuous activations are considered for MNNs. And the mixed delays which are closer to reality are taken into the system. Besides, two kinds of control schemes are proposed, including feedback and adaptive control strategies. Based on some lemmas, mathematical inequalities and the designed controllers, a few synchronization criteria are acquired. Moreover, the upper bound of settling time (ST) which is independent of the initial values is given. Finally, the feasibility of our theory is attested by simulation examples.

Neutral-type, leakage, and mixed delays in fractional-order neural networks: asymptotic synchronization analysis

<abstract><p>The dynamics of fractional-order neural networks (FONNs) are challenging to study, since the traditional Lyapunov theory does not apply to them. Instead, Halanay-type lemmas are used to create sufficient criteria for specific dynamic properties of FONNs. The application of these lemmas, however, typically leads to conservative criteria. The Halanay-type lemma is used in a novel way in this study to develop less conservative sufficient conditions in terms of linear matrix inequalities (LMIs) for extremely general FONNs, with different types of delays, such as neutral-type, leakage, time-varying, and distributed delays. The formulation of such a general model for the fractional-order scenario is done here for the first time. In addition, a new Lyapunov-like function is established, resulting in algebraic conditions that are less conservative. Three theorems are put forward that build sufficient criteria for the asymptotic synchronization, employing state feedback control, of the proposed networks, each based on a different Lyapunov-like function. For the first time in the context of FONNs, the free weighting matrix technique is also used to greatly decrease the conservatism of the obtained sufficient conditions. One numerical simulation illustrates each of the three theorems.</p></abstract>

Weighted pseudo almost periodic solutions of octonion-valued neural networks with mixed time-varying delays and leakage delays

<abstract><p>In this paper, we propose a class of octonion-valued neural networks with leakage delays and mixed delays. Considering that the multiplication of octonion algebras does not satisfy the associativity and commutativity, we can obtain the existence and global exponential stability of weighted pseudo almost periodic solutions for octonion-valued neural networks with leakage delays and mixed delays by using the Banach fixed point theorem, the proof by contradiction and the non-decomposition method. Finally, we will give one example to illustrate the feasibility and effectiveness of the main results.</p></abstract>

Robust stability and passivity analysis for discrete-time neural networks with mixed time-varying delays via a new summation inequality

<abstract><p>The summation inequality is essential in creating delay-dependent criteria for discrete-time systems with time-varying delays and developing other delay-dependent standards. This paper uses our rebuilt summation inequality to investigate the robust stability analysis issue for discrete-time neural networks that incorporate interval time-varying leakage and discrete and distributed delays. It is a novelty of this study to consider a new inequality, which makes it less conservative than the well-known Jensen inequality, and use it in the context of discrete-time delay systems. Further stability and passivity criteria are obtained in terms of linear matrix inequalities (LMIs) using the Lyapunov-Krasovskii stability theory, coefficient matrix decomposition technique, mobilization of zero equation, mixed model transformation, and reciprocally convex combination. With the assistance of the LMI Control toolbox in Matlab, numerical examples are provided to demonstrate the validity and efficiency of the theoretical findings of this research.</p></abstract>

Finite-time stochastic synchronization of fuzzy bi-directional associative memory neural networks with Markovian switching and mixed time delays via intermittent quantized control

<abstract><p>We are concerned in this paper with the finite-time synchronization problem for fuzzy bi-directional associative memory neural networks with Markovian switching, discrete-time delay in leakage terms, continuous-time and infinitely distributed delays in transmission terms. After detailed analysis, we come up with an intermittent quantized control for the concerned bi-directional associative memory neural network. By designing an elaborate Lyapunov-Krasovskii functional, we prove under certain additional conditions that the controlled network is stochastically synchronizable in finite time: The $ 1 $st moment of every trajectory of the error network system associated to the concerned controlled network tends to zero as time approaches a finite instant (the settling time) which is given explicitly, and remains to be zero constantly thereupon. In the meantime, we present a numerical example to illustrate that the synchronization control designed in this paper is indeed effective. Since the concerned fuzzy network includes Markovian jumping and several types of delays simultaneously, and it can be synchronized in finite time by our suggested control, as well as the suggested intermittent control is quantized which could reduce significantly the control cost, the theoretical results in this paper are rich in mathematical implication and have wide potential applicability in the real world.</p></abstract>

State estimation of memristor-based stochastic neural networks with mixed variable delays

State estimation of memristor-based stochastic neural networks with mixed variable delays

Pinning synchronization of dynamical neural networks with hybrid delays via event-triggered impulsive control

<abstract><p>In this study, a new event-triggered impulsive control strategy is used to solve the problem of pinning synchronization in coupled impulsive dynamical neural networks with hybrid delays. In view of discontinuous coupling terms and system dynamics, the inner delay and the impulsive delay are both investigated. Compared with the traditional pinning impulsive control, event-triggered pinning impulsive control (EPIC) generates impulse instants only when an event occurs, and is therefore more in line with practical applications. In order to deal with the complexities of mixed delays, some generalized inequalities related to hybrid delays based on Lyapunov functions are proposed, which are subject to the designed event-triggered rule. Then, in order to ensure network synchronization, linear matrix inequalities (LMIs) can provide some sufficient conditions with less conservatism while a proposed event-triggered function could successfully eliminate Zeno behavior. In addition, numerical examples are presented to prove the feasibility of the presented EPIC method.</p></abstract>

Optimal Traffic Signal Control of Isolated Oversaturated Intersections Using Predicted Demand

This paper tackles the optimal traffic signal control of isolated oversaturated intersections. An analytical signal control algorithm is proposed to find the global optimal signal timings with dynamic cycle lengths and phase splits to minimize the vehicle delay throughout the oversaturation period at a generic multi-phase junction. The traffic dynamics are modelled based on the kinematic wave theory and the predicted traffic flows. Moreover, spillback avoidance is incorporated during the queue formation oversaturated regime by adopting a mixed delay and probability of spillback objective function. Microsimulation experiments demonstrate the optimality, practicality, and robustness to system uncertainties of the proposed signal control method. The results pinpoint over 63%, 55%, and 40% reduction in total vehicle delay by implementing the proposed signal control respectively compared to an optimal fixed-time, actuated, and capacity-aware max pressure signal control methods.

Bounded real lemmas for inertial neural networks with unbounded mixed delays and state-dependent switching

This paper mainly studies the bounded real lemma for inertial neural networks with unbounded time-varying transmission delays, unbounded distribution delays and state-dependent switching. Bounded real lemmas of inertial neural networks under consideration are presented by proposing a parameterizing approach based on the system solutions. The advantage of this approach is that it neither decomposes the model into two first-order differential equations nor constructs any Lyapunov–Krasovskii functional, thus reducing computational effort and complexity. Furthermore, the obtained sufficient condition contains only a few simple linear scalar inequalities, which can be easily solved by using MATLAB. Finally, a numerical example and its numerical simulation are used to demonstrate the validity of the theoretical results.

State estimation of static neural networks with mixed delays: A new parameterized delay interval approach

This work concerns with the issue of H∞ state estimation for static neural networks with both leakage delay and time-varying delay. First, a new parameterized delay interval approach is proposed, where two parameters are introduced to divide the delay interval into four segments. Second, an appropriate Lyapunov–Krasovskii functional (LKF) including non-integral quadratic delay-product-type functional and augmented terms is constructed by combining four delay intervals. Meanwhile, for the sake of cooperating with the constructed LKF effectively, generalized free-weighting-matrix integral inequality (GFWMII) is utilized to derive much less conservative criteria. Finally, a novel criterion is derived which ensures that the considered system is asymptotically stable with prescribed H∞ performance. The effectiveness of the achieved approach is demonstrated by three commonly used numerical examples.

Global exponential bipartite synchronization for neutral memristive inertial coupling mixed time-varying delays neural networks with antagonistic interactions

In this paper, the global exponential bipartite synchronization (GEBS) for neutral-type memristive inertial coupling mixed time-varying delays neural networks (NTMI-CMTVDNNs) with synergistic and antagonistic interactions (SAI) is investigated. Firstly, the NTMI-CMTVDNNs with SAI between neurons are modeled by a signed graph. Inertial network is equivalently transformed into the first-order differential equations via variable substitution. Secondly, a novel lemma is proposed to deal with parameter mismatch of the above modeled network. By designing delay-dependent and delay-independent discontinuous control laws, the delay-dependent sufficient conditions under the bounded and unbounded activation functions are obtained to ensure the GEBS of the NTMI-CMTVDNNs with SAI with or without a leader neurons, respectively. Finally, two numerical simulation examples illustrate the validity of our theoretical results.

Quasi-projective synchronization of inertial complex-valued recurrent neural networks with mixed time-varying delay and mismatched parameters

This article investigates the quasi-projective synchronization of inertial complex-valued recurrent neural networks (ICVRNNs) with mixed time-varying delay and mismatched parameters. By using an appropriate variable transformation, the order of the ICVRNN differential system is reduced, and then, by applying the real decomposition method, it is separated into real and imaginary components. The matrix measure approach with the nonlinear Lipschitz activation functions is employed in the ICVRNN model. Through the proper description of the matrix measure approach, some sufficient conditions have been derived for the quasi-projective synchronization criteria of the considered model through designing a suitable controller. Here, some significant results have been provided for the ICVRNNs with mismatched parameters and mixed time-varying delay. Finally, two numerical simulations are discussed to validate the feasibility and persistence of our obtained results with few conditions.

Stabilization of multi-link delayed neutral-type complex networks with jump diffusion via aperiodically intermittent control

This paper focuses on the exponential stabilization of multi-link neutral-type complex networks with jump diffusion and mixed delays (MNCNJDs) via aperiodically intermittent control. Different from previous literature, several factors including multi-link, hybrid time delays and jump diffusion are all taken into consideration in our model, which makes the model more realistic. The well-known Lyapunov method is widely used in researching the stabilization issue of complex networks, and it is significant to build up an appropriate Lyapunov function for some particular problems. Consequently, in this paper, an improved Lyapunov function is established to conquer the stabilization problem of MNCNJDs. On the basis of a constructive method that integrates Lyapunov method and graph theory, some sufficient conditions are developed to ensure the stability of MNCNJDs under aperiodically intermittent control. After expounding the main results of this paper, we employ the theoretical results on stabilizing the oscillators system with jump diffusion. Ultimately, the relevant numerical simulations are presented to lend insight to demonstrate the capability and practicability of our theoretical results.

Observer-based sliding mode synchronization control of complex-valued neural networks with inertial term and mixed time-varying delays

In this paper, the synchronization problem of complex-valued inertial neural networks is studied via sliding mode control (SMC). Both mixed time-varying delays and unknown control disturbances are considered. In the absence of the equivalent transformations of real- and complex-valued systems, the systems are analyzed as an entirety form in complex domain. A disturbance observer is designed to estimate the unknown control disturbance. By constructing suitable integral switching surface function and innovative Lyapunov–Krasovskii functionals, a delay-dependent synchronization criterion is proposed on the basis of linear matrix inequality technique. An efficient SMC law based on the disturbance observer is designed, and the accessibility analysis of the predefined switching surface is provided. Eventually, numerical verification based on two types of activation functions, as well as the superiority and practicability analysis are provided.

Finite-Time and Fixed-Time Synchronization of Quaternion-Valued Neural Networks With/Without Mixed Delays: An Improved One-Norm Method.

In this article, the finite-time synchronization (FTSYN) of a class of quaternion-valued neural networks (QVNNs) with discrete and distributed time delays is studied. Furthermore, the FTSYN and fixed-time synchronization (FIXSYN) of the QVNNs without time delay are investigated. Different from the existing results, which used decomposition techniques, by introducing an improved one-norm, we use a direct analytical method to study the synchronization problems. Incidentally, several properties of one-norm of the quaternion are analyzed, and then, three effective controllers are proposed to synchronize the drive and response QVNNs within a finite time or fixed time. Moreover, efficient criteria are proposed to guarantee that the synchronization of QVNNs with or without mixed time delays can be realized within a finite and fixed time interval, respectively. In addition, the settling times are reckoned. Compared with the existing work, our advantages are mainly reflected in the simpler Lyapunov analytical process and more general activation function. Finally, the validity and practicability of the conclusions are illustrated via four numerical examples.