Multiple Time Delays Research Articles

A Car-Following Model for Connected and Automated Vehicles With Heterogeneous Time Delays Under Fixed and Switching Communication Topologies

This paper proposes a new car-following (CF) model to capture the realistic behaviors of connected and automated vehicles (CAVs), whose communication topology (CT) among vehicles is characterized by graph theory in the V2V communication environment. By considering the heterogeneous time delays under the fixed and switching CTs, a generalized CF model is proposed. Based on the Lyapunov–Krasovskii method, a convergence analysis has been implemented for this new CF model with multiple time delays to obtain the convergence condition. Meanwhile, provides an estimate of the time delay bound. Finally, numerical experiments are performed under three typical fixed CTs (i.e., PF topology, BDLF topology, and TPLF topology) and the corresponding switching topology. Results support that the proposed CF model is capable of accurately reproducing the velocity, acceleration, position, and space headway profiles of CAVs traffic flow.

RNA-sequencing and mass-spectrometry proteomic time-series analysis of T-cell differentiation identified multiple splice variants models that predicted validated protein biomarkers in inflammatory diseases.

Profiling of mRNA expression is an important method to identify biomarkers but complicated by limited correlations between mRNA expression and protein abundance. We hypothesised that these correlations could be improved by mathematical models based on measuring splice variants and time delay in protein translation. We characterised time-series of primary human naïve CD4+ T cells during early T helper type 1 differentiation with RNA-sequencing and mass-spectrometry proteomics. We performed computational time-series analysis in this system and in two other key human and murine immune cell types. Linear mathematical mixed time delayed splice variant models were used to predict protein abundances, and the models were validated using out-of-sample predictions. Lastly, we re-analysed RNA-seq datasets to evaluate biomarker discovery in five T-cell associated diseases, further validating the findings for multiple sclerosis (MS) and asthma. The new models significantly out-performing models not including the usage of multiple splice variants and time delays, as shown in cross-validation tests. Our mathematical models provided more differentially expressed proteins between patients and controls in all five diseases. Moreover, analysis of these proteins in asthma and MS supported their relevance. One marker, sCD27, was validated in MS using two independent cohorts for evaluating response to treatment and disease prognosis. In summary, our splice variant and time delay models substantially improved the prediction of protein abundance from mRNA expression in three different immune cell types. The models provided valuable biomarker candidates, which were further validated in MS and asthma.

Asymptotic stability and linear feedback control of real order systems with multiple time delays

Asymptotic stability and linear feedback control of real order systems with multiple time delays

Single-Input Single-Output System with Multiple Time Delay PID Control Methods for UAV Cluster Multiagent Systems

Multiagent has become a multidomain intersecting hot issue as artificial intelligence technology has advanced in the industrial sector. Multiagent system creation control has lately undergone a lot of academic research, and it has got applications in a wide range of fields, including drag reduction, monitoring, telecommunications relay, and searching. A matrix theory using algebraic graph theory for automatic control principle learning is proposed based on multiagent system collaborative control strategy method to study the application of PID control method in human-machine cluster multi-intelligence system. The method first presents the determination of the stability set of the low-order controller parameters for the multidelay single-input single-output system with complex coefficients; through matrix theory, the multi-intelligence system is decomposed into multiple subsystems and the problem is transformed into subsystem stability analysis problem; thus, the complexity of the system is reduced. It has been proved that the power system device adopted by the UAV hardware platform can make the UAV flight time up to 24.7 min and additional load up to 1.5 kg. Based on the simulation analysis of PID control algorithm, the PID parameters of UAV are adjusted, which improves the parameter tuning efficiency and enhances the response speed of UAV to error and the stability of motion. The experimental findings suggest that the UAV hardware platform in the UAV control system has high dynamic performance. Good PID settings allow the UAV to respond to control orders quickly and correctly; also, the data received by the sensor decrease the complexity of operating several UAVs at the same time and minimize the operators’ burden.

Adaptive neural tracking control for non‐affine switched systems with multiple time delays and actuator faults

SummaryIn this article, an adaptive output feedback neural tracking control algorithm is studied for non‐affine switched systems with multiple time delays and actuator faults. First, an adaptive neural state observer, which only needs to update a parameter online, is presented to estimate the unmeasurable state, and Lipschitz condition is used to deal with delay fault so as to avoid complex delay assumption. Then, by using online estimation information and backstepping technique, a switched fault‐tolerant control mechanism is established for non‐affine switched systems, the designed controller of each subsystems can ensure that non‐affine switched systems output signal can track reference signal under switch signals with average dwell time and all closed‐loop signals are bounded in the presence of multiple time delays, actuator faults, and external disturbances. Finally, simulation results verify the effectiveness of the proposed algorithm.

A Characterization of approximate decentralized fixed modes of time‐delay systems

AbstractThe concept of decentralized fixed mode (DFM) is crucial in determining the output feedback stabilizability by linear time‐invariant (LTI) decentralized controllers. However, in some cases, although a system has no DFMs, some of its modes may be very close to being fixed. It is thus important to characterize these modes, which are called approximate DFMs (ADFMs). In this paper, the characterization of ADFMs is discussed for LTI neutral (possibly descriptor‐type) time‐delay systems under static and dynamic decentralized output feedback control laws, and a mode mobility measure is proposed to provide quantitative information about ADFMs. To analytically compare the proposed measure, some of the commonly used quantitative measures for the characterization of ADFMs of finite‐dimensional systems have also been extended to the considered type of systems. The herein proposed approach allows multiple time delays and does not require additional expansions or preliminaries for multi‐input multi‐output systems, like some other commonly used methods. Thus, characterization with this measure, in general, requires less computational load, while it can provide more explicit information about the controller effort than the other considered measures.

Sampled-data exponential synchronization of Markovian jump chaotic Lur'e systems with multiple time delays

This paper studies the mean square exponential synchronization control of the Markovian jump chaotic Lur'e systems (MJCLSs) with multiple time delays under aperiodic sampling. Firstly, by introducing the mode-dependent single/double integral terms and considering the system state at the sampling instant, a new mode-dependent Lyapunov functional based on the looped-functional is constructed. On the basis of the constructed functional and by estimating the expectation of the solution of MJCLSs with multiple time delays, an exponential synchronization criterion in the mean square sense is presented. Then, based on the obtained stability conditions, a design method for aperiodic sampled-data controller (ASDC) to ensure the exponential synchronization is proposed. Finally, the effectiveness of the developed method is demonstrated by the Chua's circuit model and a neural network model. Compared with the existing literature, an admissible larger upper bound of sampling period can be obtained.

Coordinated Wide-Area Damping Control in Modern Power Systems Embedded with Utility-Scale Wind-Solar Plants

This paper presents a coordinated wide-area damping control of power system stabilizers (PSSs), static synchronous compensator (STATCOM), and static synchronous series compensator (SSSC) for grid-forming based wind and solar PV generation resources. The main objective of this work is to enhance the damping for inter-area oscillations while maintaining the voltage and frequency in the prescribed range, taking into consideration the operational uncertainties. Better voltage and reactive power support are provided by the use of STATCOM and for additional damping, an SSSC is employed with the coordinated wide-area damping controller (CWADC). Variable-speed wind turbine control methodology strategically combined with inertia control, de-loading control, pitch angle control, and electronic rotor speed control is employed to obtain an optimum response for discontinuous generation mixes and variable wind speed. The geometric measures of controllability/observability and residues method have been utilized to choose the appropriate input control signals and optimal location of CWADC. A multi-objective salp swarm algorithm has been used to optimize the parameters of the proposed CWADC. To demonstrate the efficacy of the proposed CWADC, nonlinear time-domain simulations are performed on a modified IEEE 68-bus test system embedded with hybrid wind-solar power plants considered multiple time delays.

Delay-based stabilisation and strong stabilisation of LTI systems by nonsmooth constrained optimisation

Stabilisation and strong stabilisation (i.e. the problem of stabilising by a stable controller) of linear time-invariant (LTI) multi-input multi-output systems are considered. The considered systems may be finite-dimensional or time-delay systems, which may have multiple discrete time delays. The controllers to be designed may also be either finite-dimensional or time-delay LTI controllers. In the controller design phase, a constrained nonsmooth optimisation-based design method is employed. The effectiveness of the proposed method is illustrated through various benchmark examples which are solved by using the recently developed Matlab-based software called DrStabilization . The examples also show that, in many cases, time-delay controllers may have certain advantages over conventional finite-dimensional controllers.

Bipartite leader-following synchronization of fractional-order delayed multilayer signed networks by adaptive and impulsive controllers

This article addresses the problem of bipartite leader-following synchronization of fractional-order delayed multilayer signed networks. It is worth emphasizing that fractional dynamics and multiple connections between nodes with multiple time delays are considered into signed networks. In our main results, adaptive control (continuous control) and impulsive control (discontinuous control) are both designed to reach the bipartite leader-following synchronization of the underlying networks. In addition, a Halanay inequality of fractional version is established. With the help of it, by using signed graph theory and Lyapunov method, some bipartite synchronization criteria are derived under the Lyapunov-type theorems and coefficients-type theorems. Then, as an application of theoretical results, the bipartite leader-following synchronization of fractional-order coupled Chua’s circuits modeled on delayed multilayer signed networks is considered. Finally, two numerical examples are exhibited to exemplify the usefulness and feasibility of the theoretical results.

State Estimation for Complex-Valued Inertial Neural Networks with Multiple Time Delays

In this paper, the problem of state estimation for complex-valued inertial neural networks with leakage, additive and distributed delays is considered. By means of the Lyapunov–Krasovskii functional method, the Jensen inequality, and the reciprocally convex approach, a delay-dependent criterion based on linear matrix inequalities (LMIs) is derived. At the same time, the network state is estimated by observing the output measurements to ensure the global asymptotic stability of the error system. Finally, two examples are given to verify the effectiveness of the proposed method.

Probing into bifurcation for fractional-order BAM neural networks concerning multiple time delays

This paper mainly examines the stability and the existence of Hopf bifurcation of fractional-order BAM neural networks with multiple delays. Based on Laplace transform, stability criterion and Hopf bifurcation theory of fractional-order differential equations, a new sufficient criterion to guarantee the stability and the existence of Hopf bifurcation for the involved fractional-order BAM neural networks with multiple delays is established. The investigation manifests that time delay plays an important role in maintaining network stability and controlling the appearance of Hopf bifurcation of fractional-order BAM neural networks. Numerical simulations are performed to check the rationality of the analytical conclusions. The obtained theoretical predictions of this paper have extremely vital guiding significance in designing and controlling networks.

Fault‐tolerant controller design for nonlinear systems with multiple input and state delays based on sliding mode algorithm

AbstractIn this article, a novel sliding mode control (SMC) strategy for nonlinear Lipschitz systems with multiple and dissimilar time delays in the states and inputs is proposed. Using linear matrix inequality, a modified integral sliding surface scientifically based on which the innovative SMC approach is developed. Lyapunov–Krasovskii's theory is employed to guarantee asymptotic stability of the closed‐loop system, such that states starting from any arbitrary initial conditions reach the sliding surface in a finite time and stay on it for all subsequent time. It is also proved that the practical effects of the actuator's faults are simultaneously attenuated. An online adaptive tuning law is used to estimate and isolate actuators' possible faults reliably. From the implementation point of view, the controller structure is more straightforward than the most existing recent fault‐tolerant control methods. Simulation results performed on practical nonlinear systems (quadruple tank and industrial continuous stirred tank reactor) verified the outstanding merits of the proposed approach. The operational capabilities of the proposed scheme in the presence of actuators' faults and multiple delays in the states and inputs were also demonstrated.

Asymptotical stability for fractional‐order Hopfield neural networks with multiple time delays

This paper is concerned with the asymptotical stability of fractional‐order Hopfield neural networks with multiple delays. The problem is actually a generalization of stability for linear fractional‐order delayed differential equations: , which is widely studied when . However, the stability is rarely known when . Hence, this work is mainly devoted to the stability analysis for . By virtue of the Laplace transform method and a decoupling technique for the characteristic equation, we propose a necessary and sufficient condition to ensure the stability, which improves the existing stability results for . Afterward, by a linearization technique, a necessary and sufficient stability condition is also presented for fractional‐order Hopfield neural networks with multiple delays. The conditions are established by delay‐independent coefficient‐type criteria. Finally, several numerical simulations are given to show the effectiveness of our results.

Multi-delay-induced bifurcation singularity in two-neuron neural models with multiple time delays

Multi-delay-induced bifurcation singularity in two-neuron neural models with multiple time delays

Mean Square Exponential Stability Analysis for Itô Stochastic Systems With Aperiodic Sampling and Multiple Time-Delays

In this article, for Itô stochastic systems with aperiodic sampling and multiple time-delays, we provide two different types of mean square exponential stability analysis methods. One method is based on the Razumikhin-type theorems method, based on this method, the mean square exponential stability criteria of the system are proposed. Meanwhile, mean square exponential practical stability criteria are also proposed. In addition, through these theorems, the constraint of positivity on the Lyapunov function for all times can be relaxed to sampling times for Itô stochastic systems with aperiodic sampling and multiple time-delays is proved. Another method is based on the looped-functionals method. Two looped-functionals are introduced to analyze the stability of Itô stochastic systems with aperiodic sampling and multiple time-delays. One functional is one-sided, while the other functional is two-sided. Based on these two functionals and the Itô formula, two mean square exponential stability criteria are presented in the form of linear matrix inequalities. Numerical examples are used to illustrate that the proposed approach is less conservative than other methods.

Relative controllability analysis of fractional order differential equations with multiple time delays

This paper is concerned with the relative controllability for a class of fractional differential equations with multiple time delays. The solution representation is introduced for this system via multiple delayed perturbations of Mittag-Leffler function. Necessary and sufficient conditions for the indicated problem to be relatively controllable are established for linear and non-linear systems. For non-linear case, the existence result is proved by using Krasnoselskii’s fixed point theorem. Numerical examples are given to illustrate the theoretical results, and its diagrammatic formulations are done by MATLAB.

Exponential Stabilization of Fuzzy Memristive Neural Networks With Multiple Time Delays Via Intermittent Control

This article investigates global exponential stabilization (GES) of Takagi–Sugeno (T–S) fuzzy memristive neural networks with multiple time-varying delays (DFMNNs) via intermittent control strategy. By resorting to differential inclusion theory, comparison means, and inequality techniques, some results are developed to ensure GES of the underlying DFMNNs via a fuzzy intermittent state feedback control law within the sense of Filippov. The outcome is generalized to GES of FMNNs with infinite distributed time delays. Additionally, the global exponential stability of FMNNs with discrete time-varying delays is explored in terms of 1-norm. The derived conditions herein contain certain existing ones as special cases. Finally, three examples are presented to illuminate the validness of the outcomes.

Global [formula omitted]-synchronization for nonlinear complex networks with unbounded multiple time delays and uncertainties via impulsive control

The global μ-synchronization problem of nonlinear drive–response complex networks with uncertainties is investigated in this paper. Unbounded multiple time delays, such as internal delays, coupling delays, and sampling delays in impulse instants are considered in our complex network model. The difficulties caused by these multiple time delays are overcome by introducing a generalized impulsive delayed comparison principle. A delayed impulsive controller is designed, and some novel synchronization criteria are derived in order to make drive–response complex networks achieve μ-synchronization. Compared with the existing related works, there is no restriction about impulse intervals and delays, as well as, the external coupling matrix is no longer needed to satisfy the dissipative coupling condition. Finally, two numerical simulations are shown to present the correctness of our theoretical results.

Controllability on a class of switched time-varying systems with impulses and multiple time delays

The problem of complete controllability is addressed for a class of switched time-varying impulsive systems under multiple input delays. Several controllability criteria are obtained with the aid of algebraic and geometric tools. Firstly, the explicit expression of solution on every impulsive interval for such systems is derived by mathematical induction and variation of parameters. Then, complete controllability is investigated for the underlying system based on the solution established. Specifically, the new necessary or/and sufficient algebraic controllability conditions are obtained without assuming that all impulse-dependent matrices are non-singular. In addition, the geometric criteria with regard to the constant matrices are further discussed when the considered system reduces to a time-invariant case. Finally, numerical examples are worked out to demonstrate the controllability tests derived in this paper. It is shown that the existence of the delayed term will potentially affect the controllability of the studied system. In contrast to the existing literatures, the criteria derived in this paper removing some constrained assumptions have less conservatism and can be used to verify the controllability of a more general linear hybrid system.