Prescribed Performance Tracking Control of Time-Delay Nonlinear Systems With Output Constraints

The problem of prescribed performance tracking control for unknown time-delay nonlinear systems subject to output constraints is dealt with in this paper. In contrast with related works, only the most fundamental requirements, i.e., boundedness and the local Lipschitz condition, are assumed for the allowable time delays. Moreover, we focus on the case where the reference is unknown beforehand, which renders the standard prescribed performance control designs under output constraints infeasible. To conquer these challenges, a novel robust prescribed performance control approach is put forward in this paper.Herein, a reverse tuning function is skillfully constructed and automatically generates a performance envelop for the tracking error. In addition, a unified performance analysis framework based on proof by contradiction and the barrier function is established to reveal the inherent robustness of the control system against the time delays. It turns out that the system output tracks the reference with a preassigned settling time and good accuracy,without constraint violations. A comparative simulation on a two-stage chemical reactor is carried out to illustrate the above theoretical findings.

Attosecond ionization time delays in strong-field physics

Electronic processes within atoms and molecules reside on the timescale of attoseconds. Recent advances in the laserbased pump-probe interrogation techniques have made possible the temporal resolution of ultrafast electronic processes on the attosecond timescale, including photoionization and tunneling ionization. These interrogation techniques include the attosecond streak camera, the reconstruction of attosecond beating by interference of two-photon transitions, and the attoclock. While the former two are usually employed to study photoionization processes, the latter is typically used to investigate tunneling ionization. In this review, we briefly overview these timing techniques towards an attosecond temporal resolution of ionization processes in atoms and molecules under intense laser fields. In particular, we review the backpropagation method, which is a novel hybrid quantum-classical approach towards the full characterization of tunneling ionization dynamics. Continued advances in the interrogation techniques promise to pave the pathway towards the exploration of ever faster dynamical processes on an ever shorter timescale.

An analytical model to estimate the time delay to reach spontaneous ignition considering heat loss in oil reservoirs

During air injection into an oil reservoir,an oxidation reaction generates some heat to raise the reservoir temperature.When the reservoir temperature reaches an ignition temperature,spontaneous ignition occurs.There is a time delay from the injection to ignition.There are mixed results regarding the feasibility of spontaneous ignition in real-field projects and in laboratory experiments.No analytical model is available in the literature to estimate the oxidation time required to reach spontaneous ignition with heat loss.This paper discusses the feasibility of spontaneous ignition from theoretical points and experimental and field project observations.An analytical model considering heat loss is proposed.Analytical models with and without heat loss investigate the factors that affect spontaneous ignition.Based on the discussion and investigations,we find that it is more difficult for spontaneous ignition to occur in laboratory experiments than in oil reservoirs;spontaneous ignition is strongly affected by the initial reservoir temperature,oil activity,and heat loss;spontaneous ignition is only possible when the initial reservoir temperature is high,the oil oxidation rate is high,and the heat loss is low.

A nonlocal dispersal and time delayed HIV infection model with general incidences

Biologically,because of the impact of reproduction period and nonlocal dispersal of HIV-infected cells,time delay and spatial heterogeneity should be considered.In this paper,we establish an HIV infection model with nonlocal dispersal and infection age.Moreover,applying the theory of Fourier transformation and von Foerster rule,we transform the model to an integrodifferential equation with nonlocal time delay and dispersal.The well-posedness,positivity,and boundedness of the solution for the model are studied.

Intelligent responsive self-assembled micro-nanocapsules:Used to delay gel gelation time

In the application of polymer gels to profile control and water shutoff,the gelation time will directly determine whether the gel can"go further"in the formation,but the most of the methods for delaying gel gelation time are complicated or have low responsiveness.There is an urgent need for an effective method for delaying gel gelation time with intelligent response.Inspired by the slow-release effect of drug capsules,this paper uses the self-assembly effect of gas-phase hydrophobic SiO_(2) in aqueous solution as a capsule to prepare an intelligent responsive self-assembled micro-nanocapsules.The capsule slowly releases the cross-linking agent under the stimulation of external conditions such as temperature and pH value,thus delaying gel gelation time.When the pH value is 2 and the concentration of gas-phase hydrophobic SiO_(2) particles is 10%,the gelation time of the capsule gel system at 30,60,90,and 120℃is12.5,13.2,15.2,and 21.1 times longer than that of the gel system without containing capsule,respectively.Compared with other methods,the yield stress of the gel without containing capsules was 78 Pa,and the yield stress after the addition of capsules was 322 Pa.The intelligent responsive self-assembled micronanocapsules prepared by gas-phase hydrophobic silica nanoparticles can not only delay the gel gelation time,but also increase the gel strength.The slow release of cross-linking agent from capsule provides an effective method for prolongating the gelation time of polymer gels.

Refinement of the Proposed Gamma-Ray Burst Time Delay Model

This paper is the second instalment in our study of the observed time delay in the arrival times of radio photons emanating from Gamma Ray Bursts (GRBs). The mundane assumption in contemporary physics as to the cause of these pondersome time delays is that they are a result of the photon being endowed with a non-zero mass. While we do not rule out the possibility of a non-zero mass for the photon, our working assumption is that the major cause of these time delays may very well be that these photons are travelling in a rarefied cosmic plasma in which the medium’s electrons interact with the electric component of the Photon, thus generating tiny currents that lead to dispersion, hence, a frequency-dependent speed of Light (FDSL). In the present instalment, we “improve” on the model presented in the first instalment by dropping the assumption that the resultant pairs of these radio photons leave the shock front simultaneously. The new assumption of a non-simultaneous— albeit systematic—emission of these photon pairs allows us to obtain a much more convincing and stronger correlation in the time delay. This new correlation allows us to build a unified model for the four GRBs in our sample using a relative distance correction mechanism. The new unified model allows us to obtain as our most significant result a value for the frequency equivalence of the interstellar medium (ISM)’s conductance ν* ~ 1.500 ± 0.009 Hzand also an independent distance measure to the GRBs where we obtain for our four GRB samples an average distance of: ~69.40 ± 0.10, 40.00 ± 0.00, 58.40 ± 0.40, and 86.00 ± 1.00 Mpc, for GRB 030329, 980425, 000418 and 021004 respectively.

Research on the Damping Mechanism of Time-Delay Coupled Negative Stiffness Dynamic Absorber in Nonlinear Vibration Damping System

A study was conducted on the effect of time delay and structural parameters on the vibration reduction of a time delayed coupled negative stiffness dynamic absorber in nonlinear vibration reduction systems. Taking dynamic absorbers with different structural and control parameters as examples, the effects of third-order nonlinear coefficients, time-delay control parameters, and negative stiffness coefficients on reducing the replication of the main system were discussed. The nonlinear dynamic absorber has a very good vibration reduction effect at the resonance point of the main system and a nearby area, and when 1 increases to a certain level, the stable region of the system continues to increase. The amplitude curve of the main system of a nonlinear dynamic absorber will generate Hop bifurcation and saddle node bifurcation in the region far from the resonance point, resulting in almost periodic motion and jumping phenomena in the system. For nonlinear dynamic absorbers with determined structural parameters, time-delay feedback control can be adopted to control the amplitude of the main system. For different negative stiffness coefficients, there exists a minimum damping point for the amplitude of the main system under the determined system structural parameters and time-delay feedback control parameters.

An improved ISR-WV rumor propagation model based on multichannels with time delay and pulse vaccination

The rapid development of the Internet has broadened the channels of dissemination of information,it has also led to the rapid and widespread propagation of rumors,which can have a serious negative impact socially.In this paper,an improved ISR-WV rumor propagation model integrating multichannels is proposed by considering the system’s time delay,and the influence of different channels of propagation on the dynamic process is further analyzed.Moreover,the basic reproduction number R0,rumor-free equilibrium,and rumor-prevailing equilibrium,as well as their stability,are deduced.Then,an optimal control problem with pulse vaccination is designed.Finally,the validity of the model and theoretical results is verified by numerical simulations and a practical application.The results show that the rumor propagation threshold R0 is more sensitive to the rate of the propagation of the information base channel.The shorter the thinking timeτ_(1)required for the ignorant to react after obtaining the information,the larger the final scale of propagation.Under this condition,the time delayτ_(2)spent by a spreader in producing a video is negatively related to the final scale of the propagation;conversely,a longerτ_(1)implies that the person tends to more cognizant,which can suppress the spread of rumors.Under this condition,τ_(2)has little effect on the final scale of propagation.In addition,the results also prove that timely implementation of the pulse vaccination control strategy of popular science education can effectively control the propagation of rumors and reduce their negative impact.

Hopf bifurcation and phase synchronization in memristor-coupled Hindmarsh–Rose and FitzHugh–Nagumo neurons with two time delays

A memristor-coupled heterogenous neural network consisting of two-dimensional(2D)FitzHugh–Nagumo(FHN)and Hindmarsh–Rose(HR)neurons with two time delays is established.Taking the time delays as the control parameters,the existence of Hopf bifurcation near the stable equilibrium point in four cases is derived theoretically,and the validity of the Hopf bifurcation condition is verified by numerical analysis.The results show that the two time delays can make the stable equilibrium point unstable,thus leading to periodic oscillations induced by Hopf bifurcation.Furthermore,the time delays in FHN and HR neurons have different effects on the firing activity of neural network.Complex firing patterns,such as quiescent state,chaotic spiking,and periodic spiking can be induced by the time delay in FHN neuron,while the neural network only exhibits quiescent state and periodic spiking with the change of the time delay in HR neuron.Especially,phase synchronization between the heterogeneous neurons is explored,and the results show that the time delay in HR neurons has a greater effect on blocking the synchronization than the time delay in FHN neuron.Finally,the theoretical analysis is verified by circuit simulations.

Synchronization of stochastic complex networks with time-delayed coupling

Noise and time delay are inevitable in real-world networks. In this article, the framework of master stability function is generalized to stochastic complex networks with time-delayed coupling. The focus is on the effects of noise, time delay,and their inner interactions on the network synchronization. It is found that when there exists time-delayed coupling in the network and noise diffuses through all state variables of nodes, appropriately increasing the noise intensity can effectively improve the network synchronizability;otherwise, noise can be either beneficial or harmful. For stochastic networks, large time delays will lead to desynchronization. These findings provide valuable references for designing optimal complex networks in practical applications.

Critical dispersion of chirped fiber Bragg grating for eliminating time delay signature of distributed feedback laser chaos

Optical chaos has attracted widespread attention owing to its complex dynamic behaviors.However,the time delay signature(TDS)caused by the external cavity mode reduces the complexity of optical chaos.We propose and numerically demonstrate the critical dispersion of chirped fiber Bragg grating(CFBG)for eliminating the TDS of laser chaos in this work.The critical dispersion,as a function of relaxation frequency and bandwidth of the optical spectrum,is found through extensive dynamics simulations.It is shown that the TDS can be eliminated when the dispersion of CFBG is above this critical dispersion.In addition,the influence of dispersive feedback light and output light from a laser is investigated.These results provide important quantitative guidance for designing chaotic semiconductor lasers without TDS.

High-Precision Time Delay Estimation Based on Closed-Form Offset Compensation

To improve the estimation accuracy,a novel time delay estimation(TDE)method based on the closed-form offset compensation is proposed.Firstly,we use the generalized cross-correlation with phase transform(GCC-PHAT)method to obtain the initial TDE.Secondly,a signal model using normalized cross spectrum is established,and the noise subspace is extracted by eigenvalue decomposition(EVD)of covariance matrix.Using the orthogonal relation between the steering vector and the noise subspace,the first-order Taylor expansion is carried out on the steering vector reconstructed by the initial TDE.Finally,the offsets are compensated via simple least squares(LS).Compared to other state-of-the-art methods,the proposed method significantly reduces the computational complexity and achieves better estimation performance.Experiments on both simulation and real-world data verify the efficiency of the proposed approach.

A True-Time-Delay Array Architecture for Wideband Multi-Beam Tracking

The true-time delay(TTD)units are critical for solving beam squint and frequency selective fading inWideband Large-Scale Antenna Systems(LSASs).In this work,we propose a TTD array architecture for wideband multi-beam tracking that eliminates the beam squint phenomenon and filters out interference signals by applying a spatial filter and time delay estimations(TDEs).The paper presents a novel approach to spatial filter design by introducing a transformation matrix that can optimize the beam response in a specific direction and at a specific frequency.Using the variable fractional delay(VFD)filters,we propose a TDE algorithm with a Newton-Raphson iteration update process that corrects the arrival time delay difference between sensors.Simulations and examples have demonstrated that the proposed architecture can achieve beam tracking within 10 ms at the low signalto-noise ratio(SNR)and demodulation loss is less than 0.5 dB in wideband multi-beam scenarios.

Time Delay Estimation in Radar System using Fuzzy Based Iterative Unscented Kalman Filter

RSs(Radar Systems)identify and trace targets and are commonly employed in applications like air traffic control and remote sensing.They are necessary for monitoring precise target trajectories.Estimations of RSs are non-linear as the parameters TDEs(time delay Estimations)and Doppler shifts are computed on receipt of echoes where EKFs(Extended Kalman Filters)and UKFs(Unscented Kalman Filters)have not been examined for computations.RSs,certain times result in poor accuracies and SNRs(low signal to noise ratios)especially,while encountering complicated environments.This work proposes IUKFs(Iterated UKFs)to track onlinefilter performances while using optimization techniques to enhance outcomes.The use of cost functions can assist state corrections while lowering costs.A new parameter is optimized using MCEHOs(Mutation Chaotic Elephant Herding Optimizations)by linearly approximating system non-linearity where OIUKFs(Optimized Iterative UKFs)predict a target's unknown parameters.To obtain optimal solutions theoretically,OIUKFs take less iteration,resulting in shorter execution times.The proposed OIUKFs provide numerical approximations which are derivative-free implementations.Simulation evaluation results with estimators show better performances in terms of reduced NMSEs(Normalized Mean Square Errors),RMSEs(Root Mean Squared Errors),SNRs,variances,and better accuracies than current approaches.

Tumor-Immune Interaction System with the Effect of Time Delay and Hyperglycemia on the Breast Cancer Cells

Breast cancer in women is a complicated and multifaceted disease. Studies have demonstrated that hyperglycemia is one of the most significant risk factors for breast cancer. Hyperglycemia is when the sugar level in human blood is too high, which means excess glucose. Glucose excess can encourage the growth, invasion, and migration of breast cancer cells at the cellular level. Though, the effects of glucose on the dynamics of breast cancer cells have been examined mathematically by a system of ordinary differential equations. However, the non-instantaneous biological occurrences leading to the secretion of immuno-suppressive cytokines by tumors to evade immune surveillance and the immune cells’ derivation of cytokines to attack the tumor cells are not yet discussed. Therefore, investigating the biological process involved in the dynamics of tumors, immune and normal cells with excessive glucose concentration is inviolable to determining the best procedure for controlling tumors’ uncontrollable growth. Time delay, denoted by τ, is used to describe the time tumor cells take to secrete immunosuppressive cytokines to evade immune surveillance and the time immune cells take to recognize and attack the tumor cells. We have studied the local stability analysis of the biological steady states in both delayed and non-delayed system. The Routh-Hurwitz stability criterion is used to analyze the dynamical equilibrium of the cells’ population. Hopf bifurcation was analyzed by using time delay s as a bifurcation parameter. The analytical results suggest an unstable scenario for a tumor-free equilibrium point as normal cells are bound to grow to their carrying capacity. The result predicts a stable system for coexisting equilibrium when the interaction is instantaneous (τ = 0). However, when τ > 0, the coexisting equilibrium point switches from stable to unstable. The numerical results not only validate all the analytical results but also show the case of possible situations when glucose concentration is varied, indicating that both tumor growth and immune system efficiency are highly affected by the level of glucose in the blood. This concluded that the delay in the secretion of cytokines by immune cells and derivation cytokines by the tumors helps to identify the possible chaotic situation under different glucose concentration and the extent to which such delay can have on restoration of the normal cells when glucose concentration is low.

Designing Proportional-Integral Consensus Protocols for Second-Order Multi-Agent Systems Using Delayed and Memorized State Information

This paper is concerned with consensus of a secondorder linear time-invariant multi-agent system in the situation that there exists a communication delay among the agents in the network.A proportional-integral consensus protocol is designed by using delayed and memorized state information.Under the proportional-integral consensus protocol,the consensus problem of the multi-agent system is transformed into the problem of asymptotic stability of the corresponding linear time-invariant time-delay system.Note that the location of the eigenvalues of the corresponding characteristic function of the linear time-invariant time-delay system not only determines the stability of the system,but also plays a critical role in the dynamic performance of the system.In this paper,based on recent results on the distribution of roots of quasi-polynomials,several necessary conditions for Hurwitz stability for a class of quasi-polynomials are first derived.Then allowable regions of consensus protocol parameters are estimated.Some necessary and sufficient conditions for determining effective protocol parameters are provided.The designed protocol can achieve consensus and improve the dynamic performance of the second-order multi-agent system.Moreover,the effects of delays on consensus of systems of harmonic oscillators/double integrators under proportional-integral consensus protocols are investigated.Furthermore,some results on proportional-integral consensus are derived for a class of high-order linear time-invariant multi-agent systems.

Primary frequency control considering communication delay for grid-connected offshore wind power systems

Offshore wind farms are becoming increasingly distant from onshore centralized control centers,and the communication delays between them inevitably introduce time delays in the measurement signal of the primary frequency control.This causes a deterioration in the performance of the primary frequency control and,in some cases,may even result in frequency instability within the power system.Therefore,a frequency response model that incorporates communication delays was established for power systems that integrate offshore wind power.The Padéapproximation was used to model the time delays,and a linearized frequency response model of the power system was derived to investigate the frequency stability under different time delays.The influences of the wind power proportion and frequency control parameters on the system frequency stability were explored.In addition,a Smith delay compensation control strategy was devised to mitigate the effects of communication delays on the system frequency dynamics.Finally,a power system incorporating offshore wind power was constructed using the MATLAB/Simulink platform.The simulation results demonstrate the effectiveness and robustness of the proposed delay compensation control strategy.

Turing Instability of Gray-Scott Reaction-Diffusion Model with Time Delay Effects

The reaction diffusion Gray-Scott model with time delay is put forward with the assumption of Neumann boundary condition is satisfied. Based on the Turing bifurcation condition, the Turing curves on two parameter plane are discussed without time delay. The normal form is computed via applying Lyapunov-Schmidt reduction method in system of PDE, and the bifurcating direction of pitchfork bifurcation underlying codimension-1 singularity of Turing point is computed. The continuation of Pitchfork bifurcation is simulated with varying free parameter continuously near the turing point, which is in coincidence with the theoritical analysis results. The wave pattern formation in the case of turing instability is also simulated which discover Turing oscillation phenomena from periodicity to irregularity.

Adaptive predictor-based control for a helicopter system with input delays:Design and experiments

In this paper,we consider a 2-degrees-of-freedom(DOF)helicopter system subject to long input delays and uncertain system parameters.To address the challenges including unknown system parameters and input delays in control design,we develop an adaptive predictor-feedback control law to achieve trajectory tracking.Stability of the closed-loop system is further established,where the tracking errors are shown to converge towards zero.Through simulation and experiments on the helicopter system,we illustrate that tracking of a desired trajectory is achieved with the proposed control scheme.

SUBSAMPLE TIME DELAY ESTIMATION BASED ON PHASE SPECTRUM OF BAND LIMITED STOCHASTIC SIGNALS

The accuracy of conventional time delay estimation （TDE） algorithms is limited by the sampling interval. A novel algorithm of subsample TDE suitable for widehand signals is presented to improve the accuracy. This algorithm applies periodogram and parabolic interpolation to the cross correlation spectrum of band limited stochastic signals, and can obtain a continuous time delay estimator. Simulations are carried out to compare the performance of the proposed algorithm with that of other subsample TDE algorithms. Results show that the proposed algorithm outperforms other algorithms and reachs the Cramer-Rao lower bound （CRLB） at a high signal- to-noise ratio. For the wideband characteristic and the randomness of the transmitting signal, the proposed algo- rithm is suitable for the low probability of intercept radars.