Search results for: excess loop delay
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 994

Search results for: excess loop delay

934 Periodic Orbits in a Delayed Nicholson's Blowflies Model

Authors: Changjin Xu, Peiluan Li

Abstract:

In this paper, a delayed Nicholson,s blowflies model with a linear harvesting term is investigated. Regarding the delay as a bifurcation parameter, we show that Hopf bifurcation will occur when the delay crosses a critical value. Numerical simulations supporting the theoretical findings are carried out.

Keywords: Nicholson's blowflies model, Stability, Hopf bifurcation, Delay.

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933 Effect of Time Delay on the Transmission of Dengue Fever

Authors: K. Patanarapelert, I.M. Tang

Abstract:

The effect of a time delay on the transmission on dengue fever is studied. The time delay is due to the presence of an incubation period for the dengue virus to develop in the mosquito before the mosquito becomes infectious. The conditions for the existence of a Hopf bifurcation to limit cycle behavior are established. The conditions are different from the usual one and they are based on whether a particular third degree polynomial has positive real roots. A theorem for determining whether for a given set of parameter values, a critical delay time exist is given. It is found that for a set of realistic values of the parameters in the model, a Hopf bifurcation can not occur. For a set of unrealistic values of some of the parameters, it is shown that a Hopf bifurcation can occur. Numerical solutions using this last set show the trajectory of two of the variables making a transition from a spiraling orbit to a limit cycle orbit.

Keywords: Dengue fever transmission, time delay, Hopfbifurcation, limit cycle behavior

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932 Time-Delay Estimation Using Cross-ΨB-Energy Operator

Authors: Z. Saidi, A.O. Boudraa, J.C. Cexus, S. Bourennane

Abstract:

In this paper, a new time-delay estimation technique based on the cross IB-energy operator [5] is introduced. This quadratic energy detector measures how much a signal is present in another one. The location of the peak of the energy operator, corresponding to the maximum of interaction between the two signals, is the estimate of the delay. The method is a fully data-driven approach. The discrete version of the continuous-time form of the cross IBenergy operator, for its implementation, is presented. The effectiveness of the proposed method is demonstrated on real underwater acoustic signals arriving from targets and the results compared to the cross-correlation method.

Keywords: Teager-Kaiser energy operator, Cross-energyoperator, Time-Delay, Underwater acoustic signals.

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931 Constructive Proof of the Existence of an Equilibrium in a Competitive Economy with Sequentially Locally Non-Constant Excess Demand Functions

Authors: Yasuhito Tanaka

Abstract:

In this paper we will constructively prove the existence of an equilibrium in a competitive economy with sequentially locally non-constant excess demand functions. And we will show that the existence of such an equilibrium in a competitive economy implies Sperner-s lemma. We follow the Bishop style constructive mathematics.

Keywords: Sequentially locally non-constant excess demand functions, Equilibrium in a competitive economy, Constructive mathematics

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930 Analysis of Time Delay Simulation in Networked Control System

Authors: Nyan Phyo Aung, Zaw Min Naing, Hla Myo Tun

Abstract:

The paper presents a PD controller for the Networked Control Systems (NCS) with delay. The major challenges in this networked control system (NCS) are the delay of the data transmission throughout the communication network. The comparative performance analysis is carried out for different delays network medium. In this paper, simulation is carried out on Ac servo motor control system using CAN Bus as communication network medium. The True Time toolbox of MATLAB is used for simulation to analyze the effect of different delays.

Keywords: NCS, Time delay, CAN Bus, True time, MATLAB.

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929 Time Delay Estimation Using Signal Envelopes for Synchronisation of Recordings

Authors: Sergei Aleinik, Mikhail Stolbov

Abstract:

In this work, a method of time delay estimation for  dual-channel acoustic signals (speech, music, etc.) recorded under  reverberant conditions is investigated. Standard methods based on  cross-correlation of the signals show poor results in cases involving  strong reverberation, large distances between microphones and  asynchronous recordings. Under similar conditions, a method based  on cross-correlation of temporal envelopes of the signals delivers a  delay estimation of acceptable quality. This method and its properties  are described and investigated in detail, including its limits of  applicability. The method’s optimal parameter estimation and a  comparison with other known methods of time delay estimation are  also provided.

 

Keywords: Cross-correlation, delay estimation, signal envelope, signal processing.

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928 Identifying Project Delay Factors in the Australian Construction Industry

Authors: Syed Sohaib Bin Hasib, Hiyam Al-Kilidar

Abstract:

Meeting project deadlines is a major challenge for most construction projects. In this study, perceptions of contractors, clients, and consultants are compared relative to a list of factors derived from the review of the extant literature on project delay. 59 causes (categorized into 8 groups) of project delays were identified from the literature. A survey was devised to get insights and ranking of these factors from clients, consultants & contractors in the Australian construction industry. Findings showed that project delays in the Australian construction industry are mainly the result of skill shortages, interference in execution, and poor coordination and communication between the project stakeholders.

Keywords: Construction, delay factors, time delay, Australian construction industry.

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927 A Characterized and Optimized Approach for End-to-End Delay Constrained QoS Routing

Authors: P.S.Prakash, S.Selvan

Abstract:

QoS Routing aims to find paths between senders and receivers satisfying the QoS requirements of the application which efficiently using the network resources and underlying routing algorithm to be able to find low-cost paths that satisfy given QoS constraints. The problem of finding least-cost routing is known to be NP hard or complete and some algorithms have been proposed to find a near optimal solution. But these heuristics or algorithms either impose relationships among the link metrics to reduce the complexity of the problem which may limit the general applicability of the heuristic, or are too costly in terms of execution time to be applicable to large networks. In this paper, we analyzed two algorithms namely Characterized Delay Constrained Routing (CDCR) and Optimized Delay Constrained Routing (ODCR). The CDCR algorithm dealt an approach for delay constrained routing that captures the trade-off between cost minimization and risk level regarding the delay constraint. The ODCR which uses an adaptive path weight function together with an additional constraint imposed on the path cost, to restrict search space and hence ODCR finds near optimal solution in much quicker time.

Keywords: QoS, Delay, Routing, Optimization

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926 Effect of Prefabricated Vertical Drain System Properties on Embankment Behavior

Authors: Seyed Abolhasan Naeini, Ali Namaei

Abstract:

This study presents the effect of prefabricated vertical drain system properties on embankment behavior by calculating the settlement, lateral displacement and induced excess pore pressure by numerical method. In order to investigate this behavior, three different prefabricated vertical drains have been simulated under an embankment. The finite element software PLAXIS has been carried out for analyzing the displacements and excess pore pressures. The results showed that the consolidation time and induced excess pore pressure are highly depended to the discharge capacity of the prefabricated vertical drain. The increase in the discharge capacity leads to decrease the consolidation process and the induced excess pore pressure. Moreover, it was seen that the vertical drains spacing does not have any significant effect on the consolidation time. However, the increase in the drains spacing would decrease the system stiffness.

Keywords: Vertical drain, prefabricated, consolidation, embankment.

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925 Bifurcations of a Delayed Prototype Model

Authors: Changjin Xu

Abstract:

In this paper, a delayed prototype model is studied. Regarding the delay as a bifurcation parameter, we prove that a sequence of Hopf bifurcations will occur at the positive equilibrium when the delay increases. Using the normal form method and center manifold theory, some explicit formulae are worked out for determining the stability and the direction of the bifurcated periodic solutions. Finally, Computer simulations are carried out to explain some mathematical conclusions.

Keywords: Prototype model, Stability, Hopf bifurcation, Delay, Periodic solution.

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924 A Current-mode Continuous-time Sigma-delta Modulator based on Translinear Loop Principle

Authors: P. Jelodarian , E. Farshidi

Abstract:

In this paper, a new approach for design of a fully differential second order current mode continuous-time sigma-delta modulator is presented. For circuit implementation, square root domain (SRD) translinear loop based on floating-gate MOS transistors that operate in saturation region is employed. The modulator features, low supply voltage, low power consumption (8mW) and high dynamic range (55dB). Simulation results confirm that this design is suitable for data converters.

Keywords: Sigma-delta, current-mode, translinear loop, geometric mean, squarer/divider.

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923 Double Loop Control of H-Bridge DC Chopper Fed Permanent Magnet DC Motor Drives Using Low Cost Hardware

Authors: Zin Maw Tun, Tun Lin Naing

Abstract:

This paper presents the two loop proportional integral (PI) controller for speed control of permanent magnet DC motor (PMDC) motor drive with H-bridge DC chopper. PMDC motors are widely used in many applications because of having a good performance and it is easy to apply the speed control. The speed can be adjusted by using armature voltage control as it had only the armature circuit. H-bridge DC chopper circuit is used to obtain the desired speed in any direction. In this system, the two loop PI controller is designed by using pole-zero cancellation method. The speed and current controller gains are considered depending on the sampling frequency of the microcontroller. An Arduino IO package is used to implement the control algorithm. Both simulation and experimental results are presented to prove the correctness of the mathematical model.

Keywords: Arduino IO package, double loop PI controller, H-bridge DC chopper, low cost hardware, PMDC motor.

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922 An Agent-Based Modelling Simulation Approach to Calculate Processing Delay of GEO Satellite Payload

Authors: V. Vicente E. Mujica, Gustavo Gonzalez

Abstract:

The global coverage of broadband multimedia and internet-based services in terrestrial-satellite networks demand particular interests for satellite providers in order to enhance services with low latencies and high signal quality to diverse users. In particular, the delay of on-board processing is an inherent source of latency in a satellite communication that sometimes is discarded for the end-to-end delay of the satellite link. The frame work for this paper includes modelling of an on-orbit satellite payload using an agent model that can reproduce the properties of processing delays. In essence, a comparison of different spatial interpolation methods is carried out to evaluate physical data obtained by an GEO satellite in order to define a discretization function for determining that delay. Furthermore, the performance of the proposed agent and the development of a delay discretization function are together validated by simulating an hybrid satellite and terrestrial network. Simulation results show high accuracy according to the characteristics of initial data points of processing delay for Ku bands.

Keywords: Terrestrial-satellite networks, latency, on-orbit satellite payload, simulation.

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921 Sliding Mode Control for Active Suspension System with Actuator Delay

Authors: Aziz Sezgin, Yuksel Hacioglu, Nurkan Yagiz

Abstract:

Sliding mode controller for a vehicle active suspension system is designed in this study. The widely used quarter car model is preferred and it is aimed to improve the ride comfort of the passengers. The effect of the actuator time delay, which may arise due to the information processing, sensors or actuator dynamics, is also taken into account during the design of the controller. A sliding mode controller was designed that has taken into account the actuator time delay by using Smith predictor. The successful performance of the designed controller is confirmed via numerical results.

Keywords: Sliding mode control, active suspension system, actuator time delay.

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920 Optimization of Communication Protocols by stochastic Delay Mechanisms

Authors: J. Levendovszky, I. Koncz, P. Boros

Abstract:

The paper is concerned with developing stochastic delay mechanisms for efficient multicast protocols and for smooth mobile handover processes which are capable of preserving a given Quality of Service (QoS). In both applications the participating entities (receiver nodes or subscribers) sample a stochastic timer and generate load after a random delay. In this way, the load on the networking resources is evenly distributed which helps to maintain QoS communication. The optimal timer distributions have been sought in different p.d.f. families (e.g. exponential, power law and radial basis function) and the optimal parameter have been found in a recursive manner. Detailed simulations have demonstrated the improvement in performance both in the case of multicast and mobile handover applications.

Keywords: Multicast communication, stochactic delay mechanisms.

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919 Ultrasonic Investigation of Molecular Interaction in Binary Liquid Mixture of Polyethylene Glycol with Ethanol

Authors: S. Grace Sahaya Sheba, R. Omegala Priakumari

Abstract:

Polyethylene glycol (PEG) is a condensation polymer of ethylene oxide and water. It is soluble in water and in many organic solvents. PEG is used to make emulsifying agents, detergents, soaps, plasticizers, ointments etc. Ethanol (C2H5OH) also known as ethyl alcohol is a well-known organic compound and has wide applications in chemical industry as it is used as a solvent for paint, varnish, in preserving biological specimens, used as a fuel mixed with petrol etc. Though their chemical and physical properties are already studied, still because of their uses in day to day life the authors thought it is better to study some more of their physical properties like ultrasonic velocity and hence adiabatic compressibility, free length, etc. A detailed study of such properties and some excess parameters like excess adiabatic compressibility, excess free volume and few more in the liquid mixtures of these two compounds with PEG as a solute and Ethanol as a solvent at various mole fractions may throw some light on deeper understanding of molecular interaction between the solute and the solvent supported by NMR, IR etc. Hence the present research work is on ultrasonics/allied studies on these two liquid mixtures. Ultrasonic velocity (U), density (ρ) and viscosity (η) at room temperature and at different mole fraction from 0 to 0.055 of ethanol in PEG have been experimentally carried out by the authors. Acoustical parameters such as adiabatic compressibility (β), free volume (Vf), acoustic impedance (Z), internal pressure (πi), intermolecular free length (Lf) and relaxation time (τ) were calculated from the experimental data. We have calculated excess parameters like excess adiabatic compressibility (βE), excess internal pressure (πiE) free length (LfE) and excess acoustic impedance (ZE) etc for these two chosen liquid mixtures. The excess compressibility is positive and maximum around a mole fraction 0.007 and excess internal pressure is negative and maximum at the same mole fraction and longer free length. The results are analyzed and it may be concluded that the molecular interactions between the solute and the solvent is not strong and it may be weak. Appropriate graphs are drawn.

Keywords: Adiabatic Compressibility, Binary mixture, Induce dipole, Polarizability, Ultrasonic.

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918 Power Reduction by Automatic Monitoring and Control System in Active Mode

Authors: Somaye Abdollahi Pour, Mohsen Saneei

Abstract:

This paper describes a novel monitoring scheme to minimize total active power in digital circuits depend on the demand frequency, by adjusting automatically both supply voltage and threshold voltages based on circuit operating conditions such as temperature, process variations, and desirable frequency. The delay monitoring results, will be control and apply so as to be maintained at the minimum value at which the chip is able to operate for a given clock frequency. Design details of power monitor are examined using simulation framework in 32nm BTPM model CMOS process. Experimental results show the overhead of proposed circuit in terms of its power consumption is about 40 μW for 32nm technology; moreover the results show that our proposed circuit design is not far sensitive to the temperature variations and also process variations. Besides, uses the simple blocks which offer good sensitivity, high speed, the continuously feedback loop. This design provides up to 40% reduction in power consumption in active mode.

Keywords: active mode, delay monitor, body biasing, VDD scaling, low power.

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917 Nitrogen Effects on Ignition Delay Time in Supersonic Premixed and Diffusion Flames

Authors: A. M. Tahsini

Abstract:

Computational study of two dimensional supersonic reacting hydrogen-air flows is performed to investigate the nitrogen effects on ignition delay time for premixed and diffusion flames. Chemical reaction is treated using detail kinetics and the advection upstream splitting method is used to calculate the numerical inviscid fluxes. The results show that just in stoichiometric condition for both premixed and diffusion flames, there is monotone dependency of the ignition delay time to the nitrogen addition. In other situations, the optimal condition from ignition viewpoint should be found using numerical investigations.

Keywords: Diffusion flame, Ignition delay time, Mixing layer, Numerical simulation, Premixed flame, Supersonic flow.

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916 Satellite Thermal Control: Cooling by a Diphasic Loop

Authors: L. Boukhris, A. Boudjemai, A. Bellar, R. Roubache, M. Bensaada

Abstract:

In space during functioning, a satellite will be heated up due to the behavior of its components such as power electronics. In order to prevent problems in the satellite, this heat has to be released in space thanks to the cooling system. This system consists of a loop heat pipe (LHP), in which a fluid streams through an evaporator and a condenser. In the evaporator, the fluid captures the heat from the satellite and evaporates. Then it flows to the condenser where it releases the heat and it condenses. In this project, the two mains parts of a cooling system are studied: the evaporator and the condenser. The study of the diphasic loop was done starting from digital simulations carried out under Matlab and Femlab.

Keywords: capillarity, condenser, evaporator, phase change, transfer of heat.

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915 An Approach for Reducing the End-to-end Delay and Increasing Network Lifetime in Mobile Adhoc Networks

Authors: R. Asokan, A. M. Natarajan

Abstract:

Mobile adhoc network (MANET) is a collection of mobile devices which form a communication network with no preexisting wiring or infrastructure. Multiple routing protocols have been developed for MANETs. As MANETs gain popularity, their need to support real time applications is growing as well. Such applications have stringent quality of service (QoS) requirements such as throughput, end-to-end delay, and energy. Due to dynamic topology and bandwidth constraint supporting QoS is a challenging task. QoS aware routing is an important building block for QoS support. The primary goal of the QoS aware protocol is to determine the path from source to destination that satisfies the QoS requirements. This paper proposes a new energy and delay aware protocol called energy and delay aware TORA (EDTORA) based on extension of Temporally Ordered Routing Protocol (TORA).Energy and delay verifications of query packet have been done in each node. Simulation results show that the proposed protocol has a higher performance than TORA in terms of network lifetime, packet delivery ratio and end-to-end delay.

Keywords: EDTORA, Mobile Adhoc Networks, QoS, Routing, TORA

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914 Delay-independent Stabilization of Linear Systems with Multiple Time-delays

Authors: Ping He, Heng-You Lan, Gong-Quan Tan

Abstract:

The multidelays linear control systems described by difference differential equations are often studied in modern control theory. In this paper, the delay-independent stabilization algebraic criteria and the theorem of delay-independent stabilization for linear systems with multiple time-delays are established by using the Lyapunov functional and the Riccati algebra matrix equation in the matrix theory. An illustrative example and the simulation result, show that the approach to linear systems with multiple time-delays is effective.

Keywords: Linear system, Delay-independent stabilization, Lyapunovfunctional, Riccati algebra matrix equation.

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913 Stability Verification for Bilateral Teleoperation System with Variable Time Delay

Authors: M. Sallam, A. Ramadan, M. Fanni, M. Abdellatif

Abstract:

Time delay in bilateral teleoperation system was introduced as a sufficient reason to make the system unstable or certainly degrade the system performance. In this paper, simulations and experimental results of implementing p-like control scheme, under different ranges of variable time delay, will be presented to verify a certain criteria, which guarantee the system stability and position tracking. The system consists of two Phantom premium 1.5A devices. One of them acts as a master and the other acts as a slave. The study includes deriving the Phantom kinematic and dynamic model, establishing the link between the two Phantoms over Simulink in Matlab, and verifying the stability criteria with simulations and real experiments.

Keywords: bilateral teleoperation, Phantom premium 1.5, varying time delay

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912 Multiple Model and Neural based Adaptive Multi-loop PID Controller for a CSTR Process

Authors: R.Vinodha S. Abraham Lincoln, J. Prakash

Abstract:

Multi-loop (De-centralized) Proportional-Integral- Derivative (PID) controllers have been used extensively in process industries due to their simple structure for control of multivariable processes. The objective of this work is to design multiple-model adaptive multi-loop PID strategy (Multiple Model Adaptive-PID) and neural network based multi-loop PID strategy (Neural Net Adaptive-PID) for the control of multivariable system. The first method combines the output of multiple linear PID controllers, each describing process dynamics at a specific level of operation. The global output is an interpolation of the individual multi-loop PID controller outputs weighted based on the current value of the measured process variable. In the second method, neural network is used to calculate the PID controller parameters based on the scheduling variable that corresponds to major shift in the process dynamics. The proposed control schemes are simple in structure with less computational complexity. The effectiveness of the proposed control schemes have been demonstrated on the CSTR process, which exhibits dynamic non-linearity.

Keywords: Multiple-model Adaptive PID controller, Multivariableprocess, CSTR process.

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911 A Grid Synchronization Phase Locked Loop Method for Grid-Connected Inverters Systems

Authors: Naima Ikken, Abdelhadi Bouknadel, Nour-eddine Tariba Ahmed Haddou, Hafsa El Omari

Abstract:

The operation of grid-connected inverters necessity a single-phase phase locked loop (PLL) is proposed in this article to accurately and quickly estimate and detect the grid phase angle. This article presents the improvement of a method of phase-locked loop. The novelty is to generate a method (PLL) of synchronizing the grid with a Notch filter based on adaptive fuzzy logic for inverter systems connected to the grid. The performance of the proposed method was tested under normal and abnormal operating conditions (amplitude, frequency and phase shift variations). In addition, simulation results with ISPM software are developed to verify the effectiveness of the proposed method strategy. Finally, the experimental test will be used to extract the result and discuss the validity of the proposed algorithm.

Keywords: Phase locked loop, PLL, notch filter, fuzzy logic control.

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910 Instability of a Nonlinear Differential Equation of Fifth Order with Variable Delay

Authors: Cemil Tunc

Abstract:

In this paper, we study the instability of the zero solution to a nonlinear differential equation with variable delay. By using the Lyapunov functional approach, some sufficient conditions for instability of the zero solution are obtained.

Keywords: Instability, Lyapunov-Krasovskii functional, delay differential equation, fifth order.

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909 Global Existence of Periodic Solutions in a Delayed Tri–neuron Network

Authors: Kejun Zhuang, Zhaohui Wen

Abstract:

In this paper, a tri–neuron network model with time delay is investigated. By using the Bendixson-s criterion for high– dimensional ordinary differential equations and global Hopf bifurcation theory for functional differential equations, sufficient conditions for existence of periodic solutions when the time delay is sufficiently large are established.

Keywords: Delay, global Hopf bifurcation, neural network, periodicsolutions.

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908 Hardware Description Language Design of Σ-Δ Fractional-N Phase-Locked Loop for Wireless Applications

Authors: Ahmed El Oualkadi, Abdellah Ait Ouahman

Abstract:

This paper discusses a systematic design of a Σ-Δ fractional-N Phase-Locked Loop based on HDL behavioral modeling. The proposed design consists in describing the mixed behavior of this PLL architecture starting from the specifications of each building block. The HDL models of critical PLL blocks have been described in VHDL-AMS to predict the different specifications of the PLL. The effect of different noise sources has been efficiently introduced to study the PLL system performances. The obtained results are compared with transistor-level simulations to validate the effectiveness of the proposed models for wireless applications in the frequency range around 2.45 GHz.

Keywords: Phase-locked loop, frequency synthesizer, fractional-N PLL, Σ-Δ modulator, HDL models

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907 Permanence and Almost Periodic Solutions to an Epidemic Model with Delay and Feedback Control

Authors: Chenxi Yang, Zhouhong Li

Abstract:

This paper is concerned with an epidemic model with delay. By using the comparison theorem of the differential equation and constructing a suitable Lyapunov functional, Some sufficient conditions which guarantee the permeance and existence of a unique globally attractive positive almost periodic solution of the model are obtain. Finally, an example is employed to illustrate our result.

Keywords: Permanence, Almost periodic solution, Epidemic model, Delay, Feedback control.

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906 An Inverse Optimal Control Approach for the Nonlinear System Design Using ANN

Authors: M. P. Nanda Kumar, K. Dheeraj

Abstract:

The design of a feedback controller, so as to minimize a given performance criterion, for a general non-linear dynamical system is difficult; if not impossible. But for a large class of non-linear dynamical systems, the open loop control that minimizes a performance criterion can be obtained using calculus of variations and Pontryagin’s minimum principle. In this paper, the open loop optimal trajectories, that minimizes a given performance measure, is used to train the neural network whose inputs are state variables of non-linear dynamical systems and the open loop optimal control as the desired output. This trained neural network is used as the feedback controller. In other words, attempts are made here to solve the “inverse optimal control problem” by using the state and control trajectories that are optimal in an open loop sense.

Keywords: Inverse Optimal Control, Radial basis function neural network, Controller Design.

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905 A Model to Study the Effect of Excess Buffers and Na+ Ions on Ca2+ Diffusion in Neuron Cell

Authors: Vikas Tewari, Shivendra Tewari, K. R. Pardasani

Abstract:

Calcium is a vital second messenger used in signal transduction. Calcium controls secretion, cell movement, muscular contraction, cell differentiation, ciliary beating and so on. Two theories have been used to simplify the system of reaction-diffusion equations of calcium into a single equation. One is excess buffer approximation (EBA) which assumes that mobile buffer is present in excess and cannot be saturated. The other is rapid buffer approximation (RBA), which assumes that calcium binding to buffer is rapid compared to calcium diffusion rate. In the present work, attempt has been made to develop a model for calcium diffusion under excess buffer approximation in neuron cells. This model incorporates the effect of [Na+] influx on [Ca2+] diffusion,variable calcium and sodium sources, sodium-calcium exchange protein, Sarcolemmal Calcium ATPase pump, sodium and calcium channels. The proposed mathematical model leads to a system of partial differential equations which have been solved numerically using Forward Time Centered Space (FTCS) approach. The numerical results have been used to study the relationships among different types of parameters such as buffer concentration, association rate, calcium permeability.

Keywords: Excess buffer approximation, Na+ influx, sodium calcium exchange protein, sarcolemmal calcium atpase pump, forward time centred space.

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