Time-delay Function Research Articles

Fermat’s least-time principle and the embedded transparent lens

We present a simplified version of the lowest-order embedded point mass gravitational lens theory and then make the extension of this theory to any embedded transparent lens. Embedding a lens effectively reduces the gravitational potential's range, i.e., partially shields the lensing potential because the lens mass is made a contributor to the mean mass density of the universe and not simply superimposed upon it. We give the time-delay function for the embedded point mass lens from which we can derive the simplified lens equation by applying Fermat's least-time principle. Even though rigorous derivations are only made for the point mass in a flat background, the generalization of the lens equation to lowest-order for any distributed lens in any homogeneous background is obvious. We find from this simplified theory that embedding can introduce corrections above the few percent level in weak lensing shears caused by large clusters but only at large impacts. The potential part of the time delay is also affected in strong lensing at the few percent level. Additionally we again confirm that the presence of a cosmological constant alters the gravitational deflection of passing photons.

On Iterative Adaptive Dynamic Programming

Linear system is very seldom in actual control works, so there is more engineering significant of researching on the actual nonlinear system. Time delay phenomenon is the objective phenomenon exists in nature. Neural network based on adaptive dynamic programming principle is selected to implement algorithm. The algorithm contains model network training, H network training for time delay function, critic network training. Before running this iterative algorithm, training the model network first, the model uses a three-layer BP network to realize. Time delay function network H(K) is to approximate the functional relationship between the current control input and the delayed input. The critic network is used to approximate system performance function. The simulation results show that the proposed iterative adaptive dynamic programming can solve for the optimal control of delay nonlinear systems.

Digital decoupling controller design for multiple time-delay continuous-time transfer function matrices

This paper presents an extended adjoint decoupling method to conduct the digital decoupling controller design for the continuous-time transfer function matrices with multiple (integer/fractional) time delays in both the denominator and the numerator matrix. First, based on the sampled unit-step response data of the afore-mentioned multiple time-delay system, the conventional balanced model-reduction method is utilised to construct an approximated discrete-time model of the original (known/unknown) multiple time-delay continuous-time transfer function matrix. Then, a digital decoupling controller is designed by utilising the extended adjoint decoupling method together with the conventional discrete-time root-locus method. An illustrative example is given to demonstrate the effectiveness of the proposed method.

Adaptive Output Feedback Control for Nonlinear Time-Delay Systems by Fuzzy Approximation Approach

In this paper, the problem of adaptive fuzzy tracking control via output feedback for a class of uncertain single-input single-output (SISO) strict-feedback nonlinear systems with unknown time-delay functions is investigated. Dynamic surface control technique is used to avoid the problem of “explosion of complexity,” which is caused by repeated differentiation of certain nonlinear functions in the backstepping design process. In addition, the fuzzy logic systems are utilized to approximate the unknown and desired control input signals directly instead of the unknown nonlinear functions. The designed controller can guarantee all the signals in the closed-loop system to be semiglobally uniformly ultimately bounded and the tracking error to converge to a small neighborhood of the origin. Simulations results are provided to demonstrate the effectiveness of the proposed methods.

Optimized Design and Analysis of Sparse-Sampling fMRI Experiments

Sparse-sampling is an important methodological advance in functional magnetic resonance imaging (fMRI), in which silent delays are introduced between MR volume acquisitions, allowing for the presentation of auditory stimuli without contamination by acoustic scanner noise and for overt vocal responses without motion-induced artifacts in the functional time series. As such, the sparse-sampling technique has become a mainstay of principled fMRI research into the cognitive and systems neuroscience of speech, language, hearing, and music. Despite being in use for over a decade, there has been little systematic investigation of the acquisition parameters, experimental design considerations, and statistical analysis approaches that bear on the results and interpretation of sparse-sampling fMRI experiments. In this report, we examined how design and analysis choices related to the duration of repetition time (TR) delay (an acquisition parameter), stimulation rate (an experimental design parameter), and model basis function (an analysis parameter) act independently and interactively to affect the neural activation profiles observed in fMRI. First, we conducted a series of computational simulations to explore the parameter space of sparse design and analysis with respect to these variables; second, we validated the results of these simulations in a series of sparse-sampling fMRI experiments. Overall, these experiments suggest the employment of three methodological approaches that can, in many situations, substantially improve the detection of neurophysiological response in sparse fMRI: (1) Sparse analyses should utilize a physiologically informed model that incorporates hemodynamic response convolution to reduce model error. (2) The design of sparse fMRI experiments should maintain a high rate of stimulus presentation to maximize effect size. (3) TR delays of short to intermediate length can be used between acquisitions of sparse-sampled functional image volumes to increase the number of samples and improve statistical power.

Exponential stability of uncertain switched systems with multiple non-differentiable time-varying delays

In this paper, the design of switching rule for exponential stability of a class of uncertain switched systems with delays is studied. The systems to be considered are linear and the state delays are time-varying. Based on Lyapunov functional and average dwell time approach, condition on the derivative of time-delay functions are not need to design switching rule for the exponential stability of switched systems with time-varying delays. The delay-dependent stability conditions are presented in terms of LMIs which can be solved easily by various available algorithms. The effectiveness of the proposed method is demonstrated by a simulation example.

Optimal Tuning of Robust Controller Based on Artificial Bee Colony Algorithm

Artificial bee colony algorithm (ABCA) is a novel swarm intelligence algorithm for global optimization. An efficient method based on ABCA is proposed for optimal tuning of robust proportional-integral-derivative (PID) controller in this paper. A multi-objective optimization is applied to balance several constraint factors of controller. Performance of robust PID controller is evaluated by a three-order and time-delay transfer function with 40%, 50% and 60% uncertainty, respectively. Simulation result clearly demonstrates that the designed controller can obtain an optimal tuning and endure parameter fluctuation. From comparisons of robust PID controller in different uncertainties, a conclusion can be obtained that performance of robust PID controller will be worse as the uncertainty increases, even obtain a divergent solution when the uncertainty is more than 60%.

비선형 상호 연결된 시간 지연 시스템을 위한 함수 예측 기법에 기반한 분산 적응 출력 궤환 제어

본 논문은 미지의 시간 지연을 갖는 비선형 상호 연결 시스템을 위한 분산 적응 출력 궤환 제어기를 제안한다. 미지의 시간 지연을 갖는 상호 연결 부분은 부시스템들의 모든 상태 변수를 포함한다. 적당한 르아브노브-크라소브스키 함수와 함수 예측 기법을 사용하여 시간 지연 함수들을 보상한다. 각각의 부시스템을 위한 시간에 독립적인 지역 제어기를 설계하기 위해 관측 동적 표면 제어 기법을 이용한다. 제어된 페루프 시스템의 모든 신호들이 준 전역적이고 균일하게 유계됨과 제어 오차가 원점 주위의 조절 가능한 주변으로 수렴함을 증명한다. This paper proposes a decentralized adaptive output-feedback controller design for nonlinear interconnected systems with unknown time delays. The interaction terms with unknown delays are related to all states of subsystems. The time-delayed functions are compensated by using appropriate Lyapunov-Krasovskii functionals and function approximation technique. The observer dynamic surface design technique is employed to design the proposed memoryless local controller for each subsystem. In addition, we prove that all signals in the closed-loop system are semiglobally uniformly bounded and control errors converge to an adjustable neighborhood of the origin.

Digital Controller Design for Analog Systems Represented by Multiple Input–Output Time-Delay Transfer Function Matrices with Long Time Delays

This paper presents a digital controller design methodology for multivariable analog systems represented by minimally realizable multiple input–output time-delay transfer function matrices with long time delays. First, the analog transfer function matrix with multiple input–output time delays is minimally realized and represented by a delay-free state-space model and a multiple output-delay function. For a specific multiple time-delay transfer function matrix with complex poles, a minimal realization scheme is newly proposed. Then the minimized delay-free state-space model is utilized for linear quadratic regulator (LQR) design. Furthermore, the designed analog LQR is digitally redesigned via a predictive state-matching method for finding a low-gain digital controller from the pre-designed high-gain analog controller. For implementation of the digitally redesigned controller, a digital observer is constructed for the multiple time-delay system with long time delays. An illustrative example is given to demonstrate the effectiveness of the proposed method.

Dynamic behavioral modeling for strongly nonlinear doherty pas using real-valued time-delay recurrent RBF model

This paper proposes a Real-Valued Time-Delay Recurrent Radial Basis Function (RVTDRRBF) model suitable for dynamic modeling of the strongly nonlinear behaviors of the Doherty Power Amplifiers (DPAs). This model has four Tapped Delay Lines (TDLs), which account for the memory effect of the DPA. The structure of the RVTDRRBF model is simpler than the traditional FeedForward Neural Networks (FFNNs) model. Weights and centers of the proposed model can be resolved by the Orthogonal Least Square (OLS) and Singular Value De-composition (SVD) algorithm. A three-carrier Wideband Code Division Multiple Access (WCDMA) signal is taken as the test signal. The simulation results in frequency-domain and time-domain for a DPA with 51 dBm output illustrate a good agreement between the RVTDRRBF model and measurement data. Moreover, comparing the Normalized Mean Square Error (NMSE) of RVTDRRBF model, memory polynomial model and RVTDRBF model, it can be noticed that the proposed RVTDRRBF model is more accurate than the RVTDRBF model and the memory polynomial model in modeling the strong dynamic nonlinearity of the DPAs.

Decentralized robust control for interconnected neutral delay systems

Decentralized robust control problem is investigated for a class of large scale neutral delay systems. The considered systems have mismatches in time delay functions. A state coordinate transformation is first employed to change the original system into a cascade system. Then the virtual linear state feedback controller is developed to stabilize the first subsystem. Based on the virtual controller, a memoryless state feedback controller is constructed for the second subsystem.

Robust Fault Detection for Nonlinear Systems with Distributed Delays

This paper focuses on the problem of robust fault detection for a class of nonlinear time-delay systems. The system under study involves distributed time delay, unknown inputs and nonlinear fault distribution functions which is dependent on the inputs, outputs and states of the system. By applying Lyapunov stability theory and free-weighting matrix methods, a novel delay-dependent sufficient condition, which is in terms of linear matrix inequality (LMI) and ensures existence of the desired robust fault detection observer for the nonlinear systems, is proposed. When the LMI is feasible, an explicit expression of a desired observer gain is given. Based on the observer technique, desired approach to robust fault detection is presented

Time-delayed autosynchronous swarm control

In this paper a general Morse potential model of self-propelling particles is considered in the presence of a time-delayed term and a spring potential. It is shown that the emergent swarm behavior is dependent on the delay term and weights of the time-delayed function, which can be set to induce a stationary swarm, a rotating swarm with uniform translation, and a rotating swarm with a stationary center of mass. An analysis of the mean field equations shows that without a spring potential the motion of the center of mass is determined explicitly by a multivalued function. For a nonzero spring potential the swarm converges to a vortex formation about a stationary center of mass, except at discrete bifurcation points where the center of mass will periodically trace an ellipse. The analytical results defining the behavior of the center of mass are shown to correspond with the numerical swarm simulations.

A general technique for the PLC-Based implementation of RW supervisors with time delay functions

The Supervisory Control Theory (SCT) introduced by Ramadge–Wonham (RW) is a general theory to design supervisors (controllers) for discrete event systems. Although over the two decades SCT has received wide attention in academia, industrial applications are very few, due to the fact that there is a discrepancy between the abstract RW supervisor and its physical implementation. In this paper, an easy to use, general and practical technique is proposed for the PLC-based implementation of RW supervisors with time delay functions. The applicability of the proposed method is demonstrated by means of a PLC-based real-time control of an experimental manufacturing system.

정지궤도 위성통신 환경모의를 위한 100 MHz 대역폭의 위성링크 시뮬레이터 개발

The transponder simulator designed to simulate the transponder of military satellite communication systems in the geostationary orbit is required to have time delay function, because of 250 ms delay time, when a radio wave transmits the distance of 36,000 km in free space. But, it is very difficult to develop 250 ms time delay device in the transponder simulator of 100 MHz bandwidth, due to unstable operation of FPGA, loss of memory data for the high speed rate signal processing. Up to date, bandwidth of the time delay device is limited to 45 MHz bandwidth. To solve this problem, we propose the new time delay techniques up to 100 MHz bandwidth without data loss. Proposed techniques are the low speed down scaling and high speed up scaling methods to read and write the external memory, and the matrix structure design of FPGA memory to treat data as high speed rate. We developed the satellite link simulator in 100 MHz bandwidth using the proposed new time delay techniques, implemented to the transponder simulator and verified the function of 265 ms time delay device in 100 MHz bandwidth.

Adaptive Fuzzy Tracking Control for MIMO Uncertain Nonlinear Time-delay Systems

Abstract This paper addresses the problem of adaptive fuzzy tracking control for MIMO uncertain nonlinear time-delay systems. The control scheme combines adaptive fuzzy control with  H control. Adaptive time-delay fuzzy logic systems are constructed and used to approximate the uncertain unknown timedelay functions. The  H compensator is designed to eliminate fuzzy approximation errors and external disturbances. The adaptive laws for parameters are given by the tracking error. The timedelay Lyapunov function is constructed, and then it is proved that the error closed loop system satisfies the anticipant  H tracking performance. Simulation results demonstrate that the control scheme is feasible.

Adaptive Neural Control of Pure-Feedback Nonlinear Time-Delay Systems via Dynamic Surface Technique

This paper is concerned with robust stabilization problem for a class of nonaffine pure-feedback systems with unknown time-delay functions and perturbed uncertainties. Novel continuous packaged functions are introduced in advance to remove unknown nonlinear terms deduced from perturbed uncertainties and unknown time-delay functions, which avoids the functions with control law to be approximated by radial basis function (RBF) neural networks. This technique combining implicit function and mean value theorems overcomes the difficulty in controlling the nonaffine pure-feedback systems. Dynamic surface control (DSC) is used to avoid "the explosion of complexity" in the backstepping design. Design difficulties from unknown time-delay functions are overcome using the function separation technique, the Lyapunov-Krasovskii functionals, and the desirable property of hyperbolic tangent functions. RBF neural networks are employed to approximate desired virtual controls and desired practical control. Under the proposed adaptive neural DSC, the number of adaptive parameters required is reduced significantly, and semiglobal uniform ultimate boundedness of all of the signals in the closed-loop system is guaranteed. Simulation studies are given to demonstrate the effectiveness of the proposed design scheme.

NEW CONCEPT OF 3.2–4.8 GHz IMPULSE GENERATOR FOR UWB TRANSMITTER

A new design of Ultra-Wide band (UWB) generator is described in this paper. The UWB impulse generator circuit is the most essential block in a mono-band UWB transmitter. The proposed ultra wide band impulse generator circuit utilizes the performances of the CMOS technology effectively, it is composed of a voltage controlled oscillator (VCO), and a rectangular pulse generator (RPG) and mixer. The RPG circuit consists of a frequency divider 1/128 circuit, time delay, N-inverters and AND gate function. The impulse UWB generator is based on the rectangular pulse modulated with the aim of generating the UWB impulse signal. This proposed circuit generates an output signal which is defined by the bandwidth of 1.6 GHz at centered frequency of 4 GHz and the limited Power Spectral Density (PSD) is −41.47 dBm/MHz. The peak-to-peak amplitude of the UWB impulse signal is 528 mV, the output impulse width of 2 ns and the impulse repetition period (PRP) is 32 ns. The power consumption is about 12.5 mW at 2.5 V voltage supply.

Output tracking for nonlinear non-minimum phase systems with output delay and application to an F-16 jet fighter

In this article, output tracking for a class of nonlinear non-minimum phase systems with output delay is considered. By applying the first-order Padé approximation technique to deal with the time-delay function, the original control problem is reduced to the output-tracking problem of a new non-minimum phase system without delay. The bounded tracking profiles of the unstable internal dynamics in the new system are generated by using the nonlinear inversion-based method, and a complete sliding mode control scheme is proposed to stabilise the output-tracking error as well as the internal dynamics. Moreover, the proposed control scheme is applied to solve the flight-path angle tracking problem of an F-16 jet fighter.

Observer-Based Robust $H_{\infty }$ Reliable Control for Uncertain T–S Fuzzy Systems With State Time Delay

In this paper, a method of robust H∞ reliable control for uncertain Takagi-Sugeno (T-S) fuzzy systems with unavailable states and time-varying delay is developed. In terms of linear-matrix inequalities (LMIs), we derive sufficient conditions for the existence of the fuzzy observer and the reliable fuzzy controller. The single-step LMI conditions, depending on the size of the delay, are proposed for the observer-based H∞ reliable controller design. This overcomes the drawback of two-step LMI approach in literature. Moreover, the designed fuzzy controller is reliable in the sense that the stability and the satisfactory performance of the closed-loop system are achieved not only under normal operation but in the presence of some actuator faults as well. The result is given without the assumption of the rate of change of time-delay function (i.e., |τ| <; 1), which makes it applicable to both slow and fast time-varying delayed systems. Without considering reliability, the proposed result is much less conservative than most of the existing results. Finally, several examples are given to show the effectiveness and advantages of our results.