Types Of Time Delays Research Articles

Dissipativity of Stochastic Competitive Neural Networks with Multiple Time Delays

The (Q,R,S)-γ-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(Q,R,S)-\\gamma -$$\\end{document}dissipative of stochastic competitive neural networks (SCNNs) with leakage delays and discrete delay is studied. Firstly, Lyapunov–Krasovskii functional is constructed, which studies the relationship between various types of time delays. Secondly, by using integral inequality technique, the linear matrix inequality (LMI) criterion of (Q,R,S)-γ-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(Q,R,S)-\\gamma -$$\\end{document}dissipative in the mean square sense of SCNNs is obtained. Furthermore, the obtained LMI criterion is extended to the passivity in the mean square sense, stability in the mean square sense, (Q,R,S)-γ-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(Q,R,S)-\\gamma -$$\\end{document}dissipative and passivity. Finally, the effectiveness of the obtained results are verified by numerical simulation.

Global co-dynamics of viral infections with saturated incidence

<abstract><p>Several mathematical models of two competing viruses (or viral strains) that have been published in the literature assume that the infection rate is determined by bilinear incidence. These models do not show co-existence equilibrium; moreover, they might not be applicable in situations where the virus concentration is high. In this paper, we developed a mathematical model for the co-dynamics of two competing viruses with saturated incidence. The model included the latently infected cells and three types of time delays: discrete (or distributed): (ⅰ) The formation time of latently infected cells; (ⅱ) The activation time of latently infected cells; (ⅲ) The maturation time of newly released virions. We established the mathematical well-posedness and biological acceptability of the model by examining the boundedness and nonnegativity of the solutions. Four equilibrium points were identified, and their stability was examined. Through the application of Lyapunov's approach and LaSalle's invariance principle, we demonstrated the global stability of equilibria. The impact of saturation incidence, latently infected cells, and time delay on the viral co-dynamics was examined. We demonstrated that the saturation could result in persistent viral coinfections. We established conditions under which these types of viruses could coexist. The coexistence conditions were formulated in terms of saturation constants. These findings offered new perspectives on the circumstances under which coexisting viruses (or strains) could live in stable viral populations. It was shown that adding the class of latently infected cells and time delay to the coinfection model reduced the basic reproduction number for each virus type. Therefore, fewer treatment efficacies would be needed to keep the system at the infection-free equilibrium and remove the viral coinfection from the body when utilizing a model with latently infected cells and time delay. To demonstrate the associated mathematical outcomes, numerical simulations were conducted for the model with discrete delays.</p></abstract>

Hopf bifurcations in an atypical p53 protein oscillator model with discrete delay or distributed delay

Human cells have a natural cancerous defense system, and p53 protein is at the core. It is well known that p53 relies on oscillatory dynamic behavior to perform tumor suppressor functions. However, the mechanism of its oscillation remains unclear. To reveal the effect of time lag on the onset of p53 oscillations, we analytically and numerically investigate a possible scenario in which p53 oscillations are driven by a time lag. The model has only three nodes, two negative loops, and one delay. We focus on two types of time delays: discrete and distributed, use Hopf bifurcation theory to derive conditions for the occurrence of limit cycle oscillations, and confirm the properties of Hopf bifurcations by normal form and central manifold approaches. The analytical results are supported by numerical results. We suggest that discrete time lag promote p53 oscillations, while distributed time lag have a dual effect on p53 oscillations. These results imply that controlling the time lag in an appropriate range favors the inhibition of p53 on cancer cells.

Stability of port-Hamiltonian systems with mixed time delays subject to input saturation

In this paper, we investigate the stability of port-Hamiltonian systems with mixed time-varying delays as well as input saturation. Three types of time delays, including state delay, input delay, and output delay, are all assumed to be bounded. By introducing the output feedback control law and utilizing serval Lyapunov–Krasovskii functionals, we present three delay-dependent stability criteria in terms of the linear matrix inequality. Meanwhile, we use Wirtinger’s inequality, constraint conditions, and Lyapunov–Krasovskii functionals of triple and quadruple integral form to obtain less conservative results. Some numerical examples demonstrate and support our results.

Synchronization of Takagi–Sugeno Fuzzy Time-Delayed Stochastic Bidirectional Associative Memory Neural Networks Driven by Brownian Motion in Pre-Assigned Settling Time

We are devoted, in this paper, to the study of the pre-assigned-time drive-response synchronization problem for a class of Takagi–Sugeno fuzzy logic-based stochastic bidirectional associative memory neural networks, driven by Brownian motion, with continuous-time delay and (finitely and infinitely) distributed time delay. To achieve the drive-response synchronization between the neural network systems, concerned in this paper, and the corresponding response neural network systems (identical to our concerned neural network systems), we bring forward, based on the structural properties, a class of control strategies. By meticulously coining an elaborate Lyapunov–Krasovskii functional, we prove a criterion guaranteeing the desired pre-assigned-time drive-response synchronizability: For any given positive time instant, some of our designed controls make sure that our concerned neural network systems and the corresponding response neural network systems achieve synchronization, with the settling times not exceeding the pre-assigned positive time instant. In addition, we equip our theoretical studies with a numerical example, to illustrate that the synchronization controls designed in this paper are indeed effective. Our concerned neural network systems incorporate several types of time delays simultaneously, in particular, they have a continuous-time delay in their leakage terms, are based on Takagi–Sugeno fuzzy logic, and can be synchronized before any pre-given finite-time instant by the suggested control; therefore, our theoretical results in this paper have wide potential applications in the real world. The conservatism is reduced by introducing parameters in our designed Lyapunov–Krasovskii functional and synchronization control.

Robust Predictor-Based Control for Multirotor UAV With Various Time Delays

This paper presents a robust predictor-based sliding mode control (RPSMC) for multirotor unmanned aerial vehicles (UAVs) to ensure desired tracking control under time delays which appear in practice by communications, complex computation, and actuator delays. Many UAV applications have difficulty in control and operation due to various types of time delays, resulting in repeated commands, severe control instability, and then mission failure. However, existing controllers have limitations in solving time delay problems. In this paper, the RPSMC with the prediction of future disturbance and reference trajectory is developed for the multirotor UAV to minimize the effects of time delay, robustly deal with external disturbances, and further achieve desired tracking control. The performance of RPSMC for the multirotor UAV is verified under various time delays and disturbances in numerical simulations. The results show the robustness and fast control convergence compared with proportional-integral-differential and conventional predictor-based controllers. Experimental results with step response and tracking of circular trajectory demonstrate the feasibility and performance of the RPSMC for UAVs in the presence of various time delays and disturbances.

Pulse Width Modulation Methods for Minimizing Commutation Torque Ripples in Low Inductance Brushless DC Motor Drives

This paper proposes pulse width modulation (PWM) methods for low inductance brushless DC (BLDC) motor drives that minimize the commutation torque ripples. An uneven current of non-commutation phase generates the commutation torque ripples. In the low inductance BLDC motor drives, two types of time delays in PWM also induce critical torque ripples. In this paper, the analyses of the time delays in PWM and their effects are introduced. Then, two PWM methods are proposed to eliminate the time delays in the commutation region and the conduction region, respectively. The commutation period is controlled to be synchronized to the switching period. In addition, the proposed methods synchronize the switching period to the commutation interrupt. As a result, the proposed methods effectively maintain the minimum commutation period as well as minimize the commutation torque ripples in the low inductance BLDC motor drives. The validity of the proposed methods is demonstrated by the simulation and experimental results in various driving conditions. The results show that the commutation period is remarkably shortened and the commutation torque ripples are reduced by 27.6% in comparison to the conventional method.

Time delays between radio and X-ray and between narrow radio bands of Sgr A* flares in the shock oscillation model

ABSTRACT We examine the time delay between radio and X-ray and between narrow radio frequency flares in Sagittarius A* (Sgr A*), from analyses of the synchrotron, bremsstrahlung, and monochromatic luminosity curves. Using the results of 2D relativistic radiation magnetohydrodynamic (MHD) simulations based on the shock oscillation model, we find three types of time delay between the synchrotron and bremsstrahlung emissions: Type A with a time delay of 2–3 h on the shock descending branch, Type B with no time delay, and Type C with an inverse time delay of 0.5–1 h on the shock ascending branch. The time delays in Types A and C are interpreted as a transit time of Alfvén and acoustic waves between both emission dominant regions, respectively. The delay times between 22 and 43 GHz flares and between 8 and 10 GHz flares are ∼13–26 and 13 min, respectively, while the inverse delay also occurs dependently on the shock location branch. These time delays between the narrow radio bands are interpreted as the transit time of the acoustic wave between the frequency-dependent effective radii $R_{\tau _{\rm \nu =1}}$, at which the optical depth τν at the accretion disc surface becomes approximately unity. The shock oscillation model explains well the observed delay times of 0.5–5 h between radio and X-ray, 20–30 min between 22 and 43 GHz, and ∼18 min between 8 and 10 GHz in Sgr A*.

Multi-Vehicle Conflict Management With Status and Intent Sharing Under Time Delays

This paper discusses conflict analysis for multiple vehicles possessing different automation levels. Two different classes of cooperation, enabled by vehicle-to-everything (V2X) communication, are considered: status-sharing and intent-sharing. Status sharing allows vehicles to exchange their instantaneous states with each other (e.g., current velocity and position), whereas intent sharing also enables information exchange regarding the future motion of vehicles (e.g., velocity and acceleration bounds). We consider two types of time delays, one in vehicle dynamics and the other in V2X communication. Using reachability theory, our conflict analysis framework interprets the information encoded in the wireless messages pertaining to the two different cooperation classes by means of conflict charts. These charts allow for efficient and reliable on-board decision making and control design for a connected automated ego vehicle which interacts with multiple connected remote vehicles when carrying out different maneuvers. We quantify the effects of time delays in a mixed-autonomy traffic environment and unveil the benefits of intent information. Utilizing real highway data, we use numerical simulations to validate the extended conflict management framework.

Point-sampled-data passivity stabilization of stochastic complex-valued memristor networks with multi-delays and reaction-diffusion term: A switching model approach

This paper focuses on the stochastic passivity problem of stochastic memristor-based complex valued neural networks with two different types of time-delays and reaction-diffusion terms by sampled-data control strategy. Different from the existing sampled-data strategies, this paper develops spatial and temporal point sampling, namely, only a finite number of points in space or time are sampled. By introducing two different Lyapunov functional and employing techniques such as Wirtinger’s integral inequality, Jensen’s inequality and Young’s inequality, etc., two different sufficient conditions for the stochastic passivity of the system are established. Prominently, the condition quantitatively reveals the relationship between the upper and lower bounds of the sampling interval at spatial and temporal points. Finally, a numerical example is given to verify the rationality of the proposed method. Notice, compared with a large number of results of real-valued reaction-diffusion neural networks, the research results of sampled-data controlled complex-valued reaction-diffusion neural networks have not appeared so far, and this work is the first attempt to fill in the gaps in this topic.

Global stabilization via output feedback of stochastic nonlinear time‐delay systems with time‐varying measurement error: A Lyapunov–Razumikhin approach

AbstractThe output feedback stabilization for a class of stochastic nonlinear systems in lower‐triangular form is discussed. The key feature of the studied systems is that both of time‐delay factors and sensor measurement error are considered into system modeling. To handle these uncertainties in unmeasured states, a form of full‐order state observer is introduced to rebuild the states of the systems. By developing a simple but efficient control scheme, a linear output feedback controller coupled with two different static gains is designed to stabilize the whole system. In contrast to the conventional Lyapunov–Krasovskii functional approach, a framework of stability analysis based on Lyapunov–Razumikhin function is proposed for the closed‐loop stochastic system. The advantage of the proposed method lies in the superior capability of tackling various types of time delays. Specially, the time derivatives of time‐delay terms can be no less than 1, or even unbounded. Finally, two examples are shown to validate our theoretical results.

Neural network based heuristic fractional order adaptive PID‐controller for eliminating communication time delay in multi‐area LFC

AbstractCommunication of interconnected power system components with each other and with control centers is provided by using various communication links. However, these links can cause significant time delays (TD) depending on the types, distance and conditions of the communication channel. In addition to temporary time delays caused by the time constants of the components due to system failures, this article draws attention to the negative effects that may be caused by permanent communication time delays in particular, as different from the literature. The communication time delays can disrupt the stable operation of power systems and even cause the whole system to breakdown by making it unstable, when combining with other delays. In the study, the fiber‐optic (F/O) links are assumed to commonly use in supervisory control and data acquisition (SCADA) systems and the communication time delays are calculated based on this scenario. However, it is no doubt that less used radio frequency (RF)‐links will create more time delays. Moreover, to eliminate the negative effects of these types of time delays, a novel neural network based‐heuristic fractional order hybrid adaptive proportional‐integral‐derivative (ML‐H‐PIλDμ) controller for multi area load frequency control (LFC) scheme is developed and analyzed.

Bifurcation Analysis of a Fractional-Order Simplicial SIRS System Induced by Double Delays

In this paper, a fractional-order susceptible-infected-recovered-susceptible (SIRS) model is studied, focusing on delay effects and high-order interactions. Two types of time delays are considered to describe latent period and healing cycle, respectively. From the ecological point of view, we found that the increasing delays caused by either the latent period or the healing cycle lead to the periodic outbreak of disease. The finding provided us with an important implication to preventing periodic outbreaks of disease by reducing the time delay, like accelerating the healing process with effective medication and medical intervention. Specifically, taking the time delays as bifurcation parameters, the stability of endemic equilibria and the existence of Hopf bifurcation are studied by analyzing the characteristic equation of the SIRS model. From a general point of view, based on the establishment of a fractional-order SIRS model, we found that the order of the fractional order is critical for describing the dynamic behavior of the model. Typically, the decrease of the order appears to bring about the disappearance of the periodic phenomenon (i.e. the periodic oscillation) of the originally stable system.

Output tracking of time-delay Hamiltonian descriptor systems under saturation constraints

In this paper, the output tracking problem of Hamiltonian descriptor systems under the influence of saturation and time delay is investigated. In order to achieve fast output tracking and reduce tracking overshoot, an extended composite nonlinear feedback (ECNF) control method is proposed for Hamiltonian descriptor systems. Considering the special form of Hamiltonian descriptor system, based on the method of model transformation, the closed-loop Hamiltonian descriptor system obtained by introducing ECNF controller is replaced by two subsystems without singularity, so as to facilitate the later processing. For two different types of time delays, the criteria of asymptotic output tracking for closed-loop Hamiltonian descriptor systems are obtained respectively. Finally, the control effect of the ECNF method is tested by selecting a practical example and a numerical example.

A frequency domain comparison of disturbance observer based control schemes

In this article, an analysis and synthesis of widely used linear disturbance observer based robust control approaches are presented. The main objective of this article is to provide an exhaustive comparison of disturbance observer based robust control approaches and to handle the structural details of each approach for gaining insight about the complexity of each approach. Toward this goal, nine performances and robustness equations portraying useful insights for understanding and analyzing control systems are derived by examining their common and equivalent block diagrams. Four of them are selected as gang of four equations, namely complementary sensitivity function, sensitivity function, disturbance sensitivity function and noise sensitivity function. Robustness and disturbance rejection performance analysis of all linear disturbance observer based control schemes and classical feedback control scheme are done using gang of four equations. With these representations, two tables discussing all prime issues and facilitating the selection of the best approach are obtained. Our research stipulates critical facts and figures of each scheme by considering the derived gang of four equations, which can be used for choosing the most appropriate disturbance observer based control approach for a given robust control problem. It is concluded that the uncertainty disturbance estimator approach is superior when time delay type uncertainty is involved in the model. Unfolding this is critical as time delay is an inevitable fact in most industrial control systems. The findings also emphasize that time domain disturbance observer based control approach is proficient if there is no process time delay.

Stability of heterogeneous traffic considering impacts of platoon management with multiple time delays

With the development of Connected Autonomous Vehicle (CAV), there will be a long-term heterogeneous traffic flow composed of Manual Vehicles (MVs) and CAVs on the road. Firstly, this study explores the traffic composition and distribution characteristics of heterogeneous traffic flow considering the limitation of communication range and CAV degradation. Secondly, we conduct a corresponding linear stability analysis for the heterogeneous traffic flow and introduce different types of time delays into the stability analysis framework. Thirdly, we verify theoretical derivation results through nonlinear numerical simulation. Finally, the influence of platoon management and time delays on the linear stability of heterogeneous traffic flow is explored. The results show that, at first, the stability of heterogeneous traffic flow deteriorates due to the involvement of CAV, and does not grow until the CAV market penetration rate reaches a certain threshold. In the speed range greater than 23.08 m/s, the heterogeneous traffic flow is constantly stable. Platoon management can significantly improve the linear stability of heterogeneous traffic flow with a high CAV market penetration rate, while time delays have a negative effect on the linear stability of heterogeneous traffic flow.

Further Results on Bifurcation for a Fractional-Order Predator-Prey System concerning Mixed Time Delays

In the present work, we mainly focus on a new established fractional-order predator-prey system concerning both types of time delays. Exploiting an advisable change of variable, we set up an isovalent fractional-order predator-prey model concerning a single delay. Taking advantage of the stability criterion and bifurcation theory of fractional-order dynamical system and regarding time delay as bifurcation parameter, we establish a new delay-independent stability and bifurcation criterion for the involved fractional-order predator-prey system. The numerical simulation figures and bifurcation plots successfully support the correctness of the established key conclusions.

Improved results on synchronization of stochastic delayed networks under aperiodically intermittent control

This paper addresses the synchronization of stochastic complex networks with time-varying delay via aperiodically intermittent control (AIC). By proposing the concepts of average control ratio and average control frequency for AIC, some new synchronization conditions are obtained, which relax the constraints of the lower bound of control widths and the upper bound of control periods. And the proportion of rest widths can be any value in (0,1). So the constraints on AIC are loosened and thus the conservativeness is reduced compared with the existing related results. Two types of time delay are investigated: (i) the upper bound of time-varying delay should be smaller than the average control width but can be larger than the lower bound of control widths; (ii) the upper bound of time-varying delay has no relationship with control and rest widths. An example of coupled stochastic oscillators systems is presented to show the effectiveness and superiority of our results.

Resilient input-to-state stable filter design for nonlinear time-delay systems

This paper is dedicated to the resilient input-to-state stable filter design for nonlinear time-delay systems subject to external disturbance input. Two types of time delay (i.e., time-variant delay and time-invariant delay) are taken into account. First, novel analysis results on input-to-state stability for the filtering error systems are presented on the basis of the Lyapunov-functional method. Both the Bessel-Legendre inequality and the reciprocally convex combination approach are employed to reduce the conservatism of the present conditions. Then, computationally tractable design strategies for the desired filters are developed via using a number of decoupling techniques. Finally, two illustrative examples are given to demonstrate the effectiveness of the input-to-state stable filter approaches for the time-variant delay case and the time-invariant delay case, respectively.

The influence of two kinds of time delays on the vibrational resonance of a fractional Mathieu–Duffing oscillator

Vibrational resonance is studied in a fractional Mathieu–Duffing oscillator with two types of time delays: fixed and distributed delays. The theoretical expression of the response amplitude is obtained by utilising the method of direct partition of slow and fast motions. Relative errors between the theoretical prediction and the numerical simulation are introduced to verify the validity of analytical approaches. The relative error of the displacement and the relative error of the response amplitude are calculated. Small relative errors show that the theoretical analysis is statistically correct. Therefore, the effects of fractional order, linear stiffness coefficient, low-frequency signal, time delay intensity and damping coefficient on the Mathieu–Duffing oscillator with distributed delay are studied successively. In order to better illustrate the impact of distributed time delay on the model, the case of fixed time delay is analysed and compared, and it can be found that the distributed delay has more significant influence than fixed delay on the system. In addition, the influence of distributed delay on the system is more significant than that of the fixed delay.