Mixed Delays Research Articles

Guaranteed Cost Control of Impulsive Nonlinear Stochastic Systems With Mixed Time Delays

ABSTRACTThis article mainly addresses the guaranteed cost control (GCC) problem for a class of impulsive nonlinear stochastic systems with mixed time delays, where both distributed time delay as well as discrete time delay are considered. Utilizing the Hamilton–Jacobi inequalities technique, Lyapunov–Krasovskii functional (LKF) and stochastic control theory, a new delay‐dependent sufficient condition is acquired to ensure the asymptotic stability in probability (ASP) of the closed‐loop system (CLS). Moreover, the guaranteed cost controller is designed and the upper bound of cost function is given. At the same time, three corollaries are presented for the special circumstance without impulse, distributed time delays or time‐varying time delay, respectively. Finally, the feasibility of the theoretical results is verified by an example.

Robust dissipativity analysis for stochastic Markov jump competitive neural networks with mixed delays

Robust dissipativity analysis for stochastic Markov jump competitive neural networks with mixed delays

State Estimation for Measurement-Saturated Memristive Neural Networks with Missing Measurements and Mixed Time Delays Subject to Cyber-Attacks: A Non-Fragile Set-Membership Filtering Framework

This paper is concerned with the state estimation problem based on non-fragile set-membership filtering for a class of measurement-saturated memristive neural networks (MNNs) with unknown but bounded (UBB) noises, mixed time delays and missing measurements (MMs), subject to cyber-attacks under the framework of weighted try-once-discard protocol (WTOD protocol). Considering bandwidth-limited open networks, this paper proposes an improved set-membership filtering based on WTOD protocol to partially solve the problem that multiple sensor-related problems and multiple network-induced phenomena influence the state estimation performance of MNNs. Moreover, this paper also discusses the gain perturbations of the estimator and proposes an improved non-fragile estimation framework based on set-membership filtering, which enhances the robustness of the estimation approach. The proposed estimation framework can effectively estimate the state of MNNs with UBB noises, estimator gain perturbations, mixed time-delays, cyber-attacks, measurement saturations and MMs. This paper first utilizes mathematical induction to provide the sufficient conditions for the existence of the desired estimator, and obtains the estimator gain by solving a set of linear matrix inequalities. Then, a recursive optimization algorithm is utilized to achieve optimal estimation performance. The effectiveness of the theoretical results is verified by comparative numerical simulation examples.

Global Stability of Phase-Change Neural Networks With Mixed Time Delays.

Phase-change memory (PCM) is a novel type of nonvolatile memory and is suitable for artificial neural synapses. This article investigates the Lagrange global exponential stability (LGES) of a class of PCNNs with mixed time delays. First, based on the conductivity characteristics of PCM, a piecewise equation is established to describe the electrical conductivity of PCM. By using the proposed piecewise equation to simulate the neural synapses, a novel PCNN with discrete and distributed time delays is proposed. Then, using comparative theory and fundamental inequalities, the LGES conditions based on the M -matrix are proposed in the sense of Filippov, and the exponential attractive set (EAS) is obtained based on M -matrix and external input. Moreover, the Lyapunov global exponential stability (GES) conditions of PCNNs without external input are obtained by using the inequality technique and eigenvalue theory, which is a form of M -matrix. Finally, two simulation examples are given to verify the validity of the obtained results.

ASYMMETRIC FUNCTIONAL-BASED APPROACHTO EXPONENTIAL STABILITY OF LINEAR DISTRIBUTEDTIME-DELAY SYSTEMS

In this paper, the problem of exponential stability of linear time-delay systems with mixed discrete and distributed delays is studied. Based on an asymmetric Lyapunov-Krasovskii functional approach, sufficient conditions are derived in terms of linear matrix inequalities to guarantee the exponential convergence of the system state trajectories with a prescribed decay rate. The efficacy of the obtained results is demonstrated by a given numerical example and simulations.

Lagrange Stability of Competitive Neural Networks with Multiple Time-Varying Delays

In this paper, the Lagrange stability of competitive neural networks (CNNs) with leakage delays and mixed time-varying delays is investigated. By constructing delay-dependent Lyapunov functional, combining inequality analysis technique, the delay-dependent Lagrange stability criterion are obtained in the form of linear matrix inequalities. And the corresponding global exponentially attractive set (GEAS) is obtained. On this basis, by exploring the relationship between the leakage delays and the discrete delay, a better GEAS of the system is obtained from the six different sizes of the two types of delays. Finally, three examples of numerical simulation are given to illustrate the effectiveness of the obtained results.

Control of blast parameters for high-quality breaking of thin slope ore bodies

Purpose. The research is aimed at substantiation of the effective method for mining thin slope ore bodies occurring in soft unstable host rocks by optimizing the breaking process, while determining the patterns of blast energy impact on the disturbed mass by explosive charges with controllable density, taking into account the geomechanical rock mass state. Methods. The research uses a comprehensive approach, including analysis of literature sources, practical experience of mining the slope ore bodies in difficult mining-geological conditions, modeling of the energy characteristics of blasts and wave action on the mass using software, as well as conducting experimental-industrial tests in the Akbakai mine. Findings. An innovative method for effective and safe ore mining from thin slope ore deposits in masses with weakened host rocks has been substantiated and developed. It implies the use of a new construction and location in the blast-holes of a charge consisting of mixed low-density explosives with widely controllable characteristics and with which the blast-holes are charged in two layers with different densities of explosives and detonated at different delay intervals. The optimum delay intervals have been determined, which improve the conditions for controlling the blast energy by changing the direction of the blast action vector towards the newly outcropped surfaces formed in the rock mass after the blasting the first stage charges. The main factors influencing the ore delivery range when mining thin slope ore bodies with blast delivery system have been revealed and methods for increasing this process efficiency are proposed. Originality. New parameters of drilling and blasting operations have been determined for the conditions of mining thin slope ore bodies of the Akbakai deposit: a rational charge construction with controllable blast characteristics has been deve-loped; the optimum range of blast-hole charging density with mixed low-density explosives and delay intervals have been substantiated; a new exponential dependence of the ore delivery range on the specific blasting agent consumption and the angle of the ore body occurrence has been revealed. Practical implications. Practical significance is in increasing the efficiency of blast breaking of minerals, improving the quality of blast delivery of broken ore to loading sites while maintaining the host rock mass continuity and reducing the ore mass dilution, eliminating the formation of large-sized pieces that complicate the blast delivery of the broken ore.

Quasi-synchronisation of conformable fractional-order complex dynamical networks with mixed delays

This paper investigates the exponential quasi-synchronisation of conformable fractional-order complex dynamical networks with mixed delays under periodically intermittent pinning control. First, by the definition of the conformable fractional-order derivative and fractional-order comparison principle, two generalised conformable fractional-order Halanay inequalities are established. Then, by these two inequalities, Lyapunov method and periodically intermittent controller, criteria for realising exponential quasi-synchronisation for the researched network are obtained. Finally, numerical examples are given to illustrate the feasibility of the derived results.

Stability and synchronization of octonion-valued neural networks with leakage and mixed delays on time scales

There has been a great deal of interest in the last few years for neural networks (NNs) with values in multidimensional domains. The most popular models are complex-valued neural networks (CVNNs), followed by quaternion-valued neural networks (QVNNs), and, more recently, by Clifford-valued neural networks (ClVNNs). However, also very recently, a different type of NNs were put forward, namely octonion-valued neural networks (OVNNs). OVNNs are defined on the 8D octonion algebra, and they are not a special type of ClVNNs, because Clifford numbers are associative, whereas octonions are not. Moreover, beside the complex and quaternion algebras, the only other normed division algebra over the reals is the algebra of octonions, which makes OVNNs a direct generalization of CVNNs and QVNNs from this point of view, raising interest for applications handling high-dimensional data. On the other hand, systems defined on time scales were proposed as a generalization of both discrete time and continuous time systems, or any type of hybrid combination between the two. Finally, time delays appear as a consequence of implementing NNs in real life circuits. Taking all these into consideration, this paper studies the fundamental properties of exponential stability and exponential synchronization for OVNNs with leakage and mixed delays defined on time scales. In order to avoid the problems raised by the non-associativity of the octonion algebra, the OVNN model is decomposed into a real-valued one. Then, two different Lyapunov-type functionals are defined and the particularities of time scale calculus are used in order to deduce sufficient conditions expressed as scalar and linear matrix inequalities (LMIs) for the exponential stability of the proposed models, based on Halanay-type inequalities suitable for time scale systems. Afterwards, a state feedback controller is used to deduce sufficient criteria given as scalar inequalities and LMIs for the exponential synchronization of the same type of models. The generality of the model, given by the definition on the algebra of octonions, the use of different types of delays, and the definition on time scales represent an important advantage. Also, for less general models, it is possible to particularize the obtained results. With the aim to demonstrate each of the paper’s four theorems, four numerical examples are provided.

Adaptive Sliding Mode Fixed-/Preassigned-Time Synchronization of Stochastic Memristive Neural Networks with Mixed-Delays

The paper addresses the fixed-/preassigned-time synchronization of stochastic memristive neural networks (MNNs) with uncertain parameters and mixed delays. Adaptive sliding mode control (ASMC) technology is mainly utilized. First, a proper sliding surface is constructed and the adaptive laws are given. Also, the synchronization control scheme is designed, which can ensure error system to realize fixed-time stability. Second, preassigned-time sliding mode control scheme is mainly provided to realize fast synchronization of MNNs. The presented theoretical methods can guarantee the error system convergence and stability for reaching and sliding mode within preassigned-time. And the synchronization criteria and explicit expression of settling time (ST) are acquired, where ST is not related with initial values and controller parameters but can be predefined perferentially. Finally, the calculation example is offered to interpret the practicability and availability of the innovations in this paper.

Adaptive finite-time synchronization of quaternion-valued inertial neural networks with mixed delays under quantized event-triggered impulsive strategy

By incorporating inertial terms, quaternions, and time-varying discrete and distributed delays into traditional neural networks (NNs), this paper establishes a category of drive-response quaternion-valued inertial neural networks (QVINNs) with mixed delays. The issue of adaptive finite-time synchronization (FTS) of the QVINNs with mixed delays is explored. To do this, a fresh and low-cost adaptive controller is devised by combining event-triggered impulsive control (ETIC) with quantized control to greatly lower the amount of communication and economic costs. In virtue of the variable substitution, the Lyapunov method, the comparison principle, the inequality technique, and the concept of average impulsive interval (AII), the novel criteria that the QVINNs can accomplish FTS are derived. Meanwhile, it is possible to determine that Zeno-behavior and chattering are absent, and the settling time is predicted. Ultimately, by performing the numerical instance, the efficiency and accuracy of the theoretical results are confirmed.

[formula omitted] anti-synchronization of switching inertial neural networks with leakage delays and mixed time-varying delays

In this paper, the H∞ anti-synchronization problem of switching inertial neural networks with constant leakage delays and time-varying mixed delays is addressed. A direct analysis method based on parameterized system solutions is proposed to solve the problem we studied. The advantages of this method are that the variable substitution is not required for the system model and no Lyapunov–Krasovskii functional is constructed, which simplifies the proof process. In addition, the resulting anti-synchronization conditions consisting of some simple scalar inequalities can be easily solved by business softwares, and less computational complexity is involved. It is worth noting that the problem addressed in this paper has not been studied at present, and the limitation on the parity of activation functions in the existing literatures is removed, which reduces conservativeness. Finally, the reliability of the theoretical results is verified by numerical simulations.

A novel direct method to [formula omitted] synchronization of switching inertial neural networks with mixed time-varying delays

In this paper, the H∞ synchronization problem of switching inertial neural networks with mixed time-varying delays is discussed. A parameterized system solution-based direct analysis method combined with minimum residence time method is proposed to solve the considered problem. The advantage of this method is that no model transformation or construction of Lyapunov–Krasovskii functional is required, thus reducing the complexity of derivation process. In addition, the resulting synchronization conditions composed of some simple scalar inequalities can be easily solved via MATLAB. Finally, the reliability of the theoretical results is illustrated by numerical simulations.

Global exponential synchronization of BAM memristive neural networks with mixed delays and reaction–diffusion terms

Based on m-norm, this paper investigates global exponential synchronization (GES) for BAM memristive neural networks (BAMMNNs) with mixed delays and reaction–diffusion (RD) terms. Different from the existing literatures, this paper discusses the GES of the NNs based on a new integral inequality with infinite distributed delay. This method is based on inequality technique and comparison principle, which makes the form of Lyapunov function and controller more simple. Next, by introducing two different control strategies and the concept of driven response, two sufficient conditions are got to ensure GES of the proposed system. It is noteworthy that the results obtained by algebraic inequality are extension of the previous conclusions. Finally, two instances verify the correctness of the conclusions.

Distributed State Estimation for Mixed Delays System Over Sensor Networks With Multichannel Random Attacks and Markov Switching Topology.

This article deals with the distributed state estimation for mixed delays system under unknown attacks. A new multichannel random attack model is established for the first time, where network attacks are considered to exist in three channels: the target-to-sensor channel, the senor-to-sensor channel, and the sensor-to-estimator channel. In the above model, transmitted packets are allowed to be attacked multiple times simultaneously, and when they are successfully attacked, the transmitted information is modified. Besides, the topology of the sensor network is considered to change dynamically according to the Markov chain. Based on the newly established distributed estimation model, the estimation error system is proven to be asymptotically mean-square stable under a given H∞ antidisturbance index by using a Lyapunov theory and a stochastic analysis technique; then, the estimator parameter matrices are solved utilizing a linearization method. Finally, several simulation examples are listed to testify the effectiveness of the designed algorithm.

Global robust exponential synchronization of neutral-type interval Cohen–Grossberg neural networks with mixed time delays

Global robust exponential synchronization of neutral-type interval Cohen–Grossberg neural networks (NTICGNNs) with mixed time delays is analyzed in this paper. The system model, in which unrepresentable using vector-matrices, renders certain methods unsuitable for addressing issues within the vector-matrix framework. To address this limitation, a direct method based on system solutions is proposed, and sufficient conditions are provided to achieve global robust exponential synchronization of the considered NTICGNNs. This approach results in a global robust exponential synchronization criterion without the need to establish any Lyapunov-Krasovskii functionals. The applicability of the obtained synchronization conditions is validated using two numerical examples. Additionally, the obtained theoretical results have been applied to solve a quadratic programming problem and to encrypt and decrypt color images, demonstrating the practical application value of our research results. Notably, this study presents the first global robust exponential synchronization analysis for the considered NTICGNNs and proposes a novel approach grounded in system solutions.

Synchronization of Fractional Delayed Memristive Neural Networks with Jump Mismatches via Event-Based Hybrid Impulsive Controller

This study investigates the asymptotic synchronization in fractional memristive neural networks of the Riemann–Liouville type, considering mixed time delays and jump mismatches. Addressing the challenges associated with discrepancies in the circuit switching speed and the accuracy of the memristor, this paper introduces an enhanced model that effectively navigates these complexities. We propose two novel event-based hybrid impulsive controllers, each characterized by unique triggering conditions. Utilizing advanced techniques in inequality and hybrid impulsive control, we establish the conditions necessary for achieving synchronization through innovative Lyapunov functions. Importantly, the developed controllers are theoretically optimized to minimize control costs, an essential consideration for their practical deployment. Finally, the effectiveness of our proposed approach is demonstrated through two illustrative simulation examples.

Asymptotic Behavior of Some Differential Inequalities with Mixed Delays and Their Applications

In this paper, we focus on the asymptotic stability of the trajectories governed by the differential inequalities with mixed delays using the fixed-point theorem. It is interesting that the Halanay inequality is a special case of the differential inequality studied in this paper. Our results generalize and improve the existing results on Halanay inequality. Finally, three numerical examples are utilized to illustrate the effectiveness of the obtained results.

Exponential stabilization of the class of the switched systems with mixed time varying delays in state and control

This paper presents the problem of exponential stabilization of switched systems with mixed time-varying delays in state and control. Based on the partitioning of the stability state regions into convex cones, a constructive geometric design for switching laws is put forward. By using an improved Lyapunov–Krasovskii functional in combination with matrix knowledge, we design a state feedback controller that guarantees the closed-loop system to be exponentially stable. The obtained conditions are given in terms of linear matrix inequalities (LMIs), which can be effectively decoded in polynomial time by various computational tools such as the LMI tool in MATLAB software. A numerical example is proposed to illustrate the effectiveness of the obtained results.

Dissipativity Analysis of Memristive Inertial Competitive Neural Networks with Mixed Delays

Without altering the inertial system into the two first-order differential systems, this paper primarily works over the global exponential dissipativity (GED) of memristive inertial competitive neural networks (MICNNs) with mixed delays. For this purpose, a novel differential inequality is primarily established around the discussed system. Then, by applying the founded inequality and constructing some novel Lyapunov functionals, the GED criteria in the algebraic form and the linear matrix inequality (LMI) form are given, respectively. Furthermore, the estimation of the global exponential attractive set (GEAS) is furnished. Finally, a specific illustrative example is analyzed to check the correctness and feasibility of the obtained findings.