Search results for: associated linear equations ALEs

Authors: Nan Tang, Bin Wu, Cunfu He

Abstract:

The trapezoid rods are widely used in civil engineering as load –carrying members. Ultrasonic guided wave is one of the most popular techniques in analyzing the propagation of elastic guided wave. The goal of this paper is to investigate the propagation of elastic waves in the isotropic bar with trapezoid cross-section. Dispersion curves that describe the relationship between the frequency and velocity provide the fundamental information to describe the propagation of elastic waves through a structure. Based on the SAFE (semi-analytical finite element) a linear algebraic system of equations is obtained. By using numerical methods, dispersion curves solved for the rods with the trapezoid cross-section. These fundamental information plays an important role in applying ultrasonic guided waves to NTD for structures with trapezoid cross section.

Keywords: guided wave, dispersion, finite element method, trapezoid rod

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Authors: Oliver Takawira, Thembi Hope

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This study will analyse the relationship between Bitcoin price movements and the Johannesburg stock exchange (JSE). The aim is to determine whether Bitcoin price movements affect the stock market performance. As crypto currencies continue to gain prominence as a safe asset during periods of economic distress, this raises the question of whether Bitcoin’s prosperity could affect investment in the stock market. To identify the existence of a short run and long run linear relationship, the study will apply the Autoregressive Distributed Lag Model (ARDL) bounds test and a Vector Error Correction Model (VECM) after testing the data for unit roots and cointegration using the Augmented Dicker Fuller (ADF) and Phillips-Perron (PP). The Non-Linear Auto Regressive Distributed Lag (NARDL) will then be used to check if there is a non-linear relationship between bitcoin prices and stock market prices.

Keywords: bitcoin, stock market, interest rates, ARDL

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Authors: Munawwar Mohabuth, Andrei Kotousov, Ching-Tai Ng

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On the basis of the finite deformation theory, the effect of homogeneous stress on the propagation of Lamb waves in an initially isotropic hyperelastic plate is analysed. The equations governing the propagation of small amplitude waves in the prestressed plate are derived using the theory of small deformations superimposed on large deformations. By enforcing traction free boundary conditions at the upper and lower surfaces of the plate, acoustoelastic dispersion equations for Lamb wave propagation are obtained, which are solved numerically. Results are given for an aluminum plate subjected to a range of applied stresses.

Keywords: acoustoelasticity, dispersion, finite deformation, lamb waves

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Authors: T. T. Tham

Abstract:

The aim of this study is to propose an integrated approach to determine the most suitable programs, based on Quality Function Deployment (QFD), Sensitivity Analysis (SA) and Multi-Objective Linear Programming model (MOLP). Firstly, QFD is used to determine business requirements and transform them into business and supply chain programs. From the QFD, technical scores of all programs are obtained. All programs are then evaluated through five criteria (productivity, quality, cost, technical score, and feasibility). Sets of weight of these criteria are built using Sensitivity Analysis. Multi-Objective Linear Programming model is applied to select suitable programs according to multiple conflicting objectives under a budget constraint. A case study from the Sai Gon-Mien Tay Beer Company is given to illustrate the proposed methodology. The outcome of the study provides a comprehensive picture for companies to select suitable programs to obtain the optimal solution according to their preference.

Keywords: business program, multi-objective linear programming model, quality function deployment, sensitivity analysis, supply chain management

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Authors: Sonia Sonia

Abstract:

This paper presents a family of iterative scheme for solving nonlinear systems of equations which have wide application in sciences and engineering. The proposed iterative family is based upon some parameters which generates many different iterative schemes. This family is completely derivative free and uses first of divided difference operator. Moreover some numerical experiments are performed and compared with existing methods. Analysis of convergence shows that the presented family has fourth-order of convergence. The dynamical behaviour of proposed family and local convergence have also been discussed. The numerical performance and convergence region comparison demonstrates that proposed family is efficient.

Keywords: convergence, divided difference operator, nonlinear system, Newton's method

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Authors: Yongjian Du, Jinhua Sun, Kim M. Liew, Huahua Xiao

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Optimal allocation of emergency resources before a disaster is of great importance for emergency response. In reality, the pre-protection for a single critical node where accidents may occur is common. In this study, a model is developed to determine location and inventory decisions of multiple emergency resources among a set of candidate stations to minimize the total cost based on the constraints of budgetary and capacity. The total cost includes the economic accident loss which is accorded with probability distribution of time and the warehousing cost of resources which is increasing over time. A ratio is set to measure the degree of a storage station only serving the target node that becomes larger with the decrease of the distance between them. For the application of linear program, it is assumed that the length of travel time to the accident scene of emergency resources has a linear relationship with the economic accident loss. A computational experiment is conducted to illustrate how the proposed model works, and the results indicate its effectiveness and practicability.

Keywords: emergency response, integer linear program, multiple emergency resources, pre-allocation decisions, single potential accident node

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Authors: M. Khoshab, M. J. Sedigh

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Dynamic systems, which in mathematical point of view are those governed by differential equations, are much more difficult to study and to predict their behavior in comparison with static systems which are governed by algebraic equations. Economical systems such as market are among complicated dynamic systems. This paper tries to adopt a very simple mathematical model for market and to study effect of supply and demand function on behavior of the market while the supply side experiences a lag due to production restrictions.

Keywords: dynamic system, lag on supply demand, market stability, supply demand model

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Authors: Saleh Elawgali

Abstract:

Current spectrums of a four pole-pair, 400 kW induction machine were calculated for the cases of full symmetry and static eccentricity. The calculations involve integration of 93 electrical plus four mechanical ordinary differential equations. Electrical equations account for variable inductances affected by slotting and eccentricities. The calculations were followed by Fourier analysis of the stator currents in steady state operation. Zooms of the current spectrums, around the 50 Hz fundamental harmonic as well as of the main slot harmonic zone, were included. The spectrums included refer to both calculated and measured currents.

Keywords: diagnostic, harmonic, induction machine, spectrum

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Authors: Gonzalez Carlos, Martinez Fransisco

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There are various types of analysis that allow us to involve seismic phenomena that cause strong requirements for structures that are designed by society; one of them is a probabilistic analysis which works from prediction equations that have been created based on metadata seismic compiled in different regions. These equations form models that are used to describe the 5% damped pseudo spectra response for the various zones considering some easily known input parameters. The biggest problem for the creation of these models requires data with great robust statistics that support the results, and there are several places where this type of information is not available, for which the use of alternative methodologies helps to achieve adjustments to different models of seismic prediction.

Keywords: GMPM, 5% damped pseudo-response spectra, models of seismic prediction, PSHA

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Authors: Dechrit Maneetham

Abstract:

Pick and place task is one among the most important tasks in industrial field handled by 'Selective Compliance Assembly Robot Arm' (SCARA). Repeatability with high-speed movement in a horizontal plane is a remarkable feature of this type of manipulator. The challenge of design SCARA is the difficulty of achieving stability of high-speed movement with the long length of links. Shorter links arm can move more stable. This condition made the links should be considered restrict then followed by restriction of operation area (workspace). In this research, authors demonstrated on expanding SCARA robot’s workspace in horizontal area via linear sliding actuator that embedded to base link of the robot arm. With one additional prismatic joint, the previous robot manipulator with 3 degree of freedom (3-DOF), 2 revolute joints and 1 prismatic joint becomes 4-DOF PRRP manipulator. This designation increased workspace of robot from 0.5698m² performed by the previous arm (without linear actuator) to 1.1281m² by the proposed arm (with linear actuator). The increasing rate was about 97.97% of workspace with the same links' lengths. The result of experimentation also indicated that the operation time spent to reach object position was also reduced.

Keywords: kinematics, linear sliding actuator, manipulator, control system

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Authors: Avinash Kharel

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Background: - Linear sprint training is one possible approach to developing sprint performance, a crucial skill to focus on in soccer. Numerous methods, including various on-field training options, can be employed to attain this goal. However, the effect of In-season linear sprint training on sprint performance and related kinetics changes are unknown in a professional setting. The study aimed to investigate the effect of in-season linear sprint training on the sprint kinematics of amateur soccer players. Methods: - After familiarization, a 4-week training protocol was completed with sprint performance and Force Velocity (FV) profiles was compared before and after the training. Eighteen amateur soccer male players (Age 22 ± 2 years: Height: 178 ± 7cm; body-mass: 74 ± 8 Kg, 30-m split-time: 4.398 ± s) participated in the study. Sprint kinematics variables, including maximum Sprint Velocity (V0), Theoretical Maximum Force (F0), Maximum Force Output per kilogram of body weight (N/KG), Maximum Velocity (V(0)), Maximum Power Output (P MAX (W)), Ratio of Force to Velocity (FV), and Ratio of Force to Velocity at Peak power were measured. Results: - Results showed significant improvements in Maximum Sprint Velocity (p<0.01, ES=0.89), Theoretical Maximum Force (p<0.05, ES=0.50), Maximum Force Output per kilogram of body weight (p<0.05, ES=0.42), Maximum Power Output (p<0.05, ES=0.52), and Ratio of Force to Velocity at Peak Power (RF PEAK) (p<0.05, ES=0.44) post-training. There were no significant changes in the ratio of Force to Velocity (FV) and Maximum Velocity V (0) post-training (p>0.05). Conclusion: - These findings suggest that In-season linear sprint training can effectively improve certain sprint kinematics variables in amateur soccer players. Coaches and players should consider incorporating linear sprint training into their in-season training programs to improve sprint performance.

Keywords: sprint performance, training intervention, soccer, kinematics

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Authors: Somveer Singh, Vineet Kumar Singh

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We present a new model based on viscoelasticity for the Non-Newtonian fluids.We use a matrix formulated algorithm to approximate solutions of a class of partial integro-differential equations with the given initial and boundary conditions. Some numerical results are presented to simplify application of operational matrix formulation and reduce the computational cost. Convergence analysis, error estimation and numerical stability of the method are also investigated. Finally, some test examples are given to demonstrate accuracy and efficiency of the proposed method.

Keywords: Legendre Wavelets, operational matrices, partial integro-differential equation, viscoelasticity

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Authors: M. Khairudin

Abstract:

This paper investigates the system identification and design quantitative feedback theory (QFT) for the robust control of a lathe spindle. The dynamic of the lathe spindle is uncertain and time variation due to the deepness variation on cutting process. System identification was used to obtain the dynamics model of the lathe spindle. In this work, real time system identification is used to construct a linear model of the system from the nonlinear system. These linear models and its uncertainty bound can then be used for controller synthesis. The real time nonlinear system identification process to obtain a set of linear models of the lathe spindle that represents the operating ranges of the dynamic system. With a selected input signal, the data of output and response is acquired and nonlinear system identification is performed using Matlab to obtain a linear model of the system. Practical design steps are presented in which the QFT-based conditions are formulated to obtain a compensator and pre-filter to control the lathe spindle. The performances of the proposed controller are evaluated in terms of velocity responses of the the lathe machine spindle in corporating deepness on cutting process.

Keywords: lathe spindle, QFT, robust control, system identification

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Authors: Khawar Ali

Abstract:

We present the numerical study of unsteady hydromagnetic (MHD) flow and heat transfer characteristics of a viscous incompressible electrically conducting water-based hybrid metallic nanofluid (containing Cu-Au/ H₂O nanoparticles) between two orthogonally moving porous coaxial disks with suction. Different from the classical shooting methodology, we employ a combination of a direct and an iterative method (SOR with optimal relaxation parameter) for solving the sparse systems of linear algebraic equations arising from the FD discretization of the linearized self similar nonlinear ODEs. Effects of the governing parameters on the flow and heat transfer are discussed and presented through tables and graphs. The findings of the present investigation may be beneficial for the electronic industry in maintaining the electronic components under effectiveand safe operational conditions.

Keywords: heat transfer enhancement, hybrid metallic nanofluid, viscous dissipation and joule heating effect , Two dimensional flow

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Authors: Maryam Ebrahimpour, Amir Ebrahimi

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This paper presents the steady-state amplitude analysis of MOS Colpitts oscillator with short channel device. The proposed method is based on a large signal analysis and the nonlinear differential equations that govern the oscillator circuit behaviour. Also, the short channel effects are considered in the proposed analysis and analytical equations for finding the steady-state oscillation amplitude are derived. The output voltage calculated from this analysis is in excellent agreement with simulations for a wide range of circuit parameters.

Keywords: colpitts oscillator, CMOS, electronics, circuits

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Authors: S. Khan, A. Khan, Abdul R. Soomrani, Raja F. Zafar, A. Waqas, G. Akbar

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This paper proposes a low-complexity image interpolation method. Image interpolation is used to convert a low dimension video/image to high dimension video/image. The objective of a good interpolation method is to upscale an image in such a way that it provides better edge preservation at the cost of very low complexity so that real-time processing of video frames can be made possible. However, low complexity methods tend to provide real-time interpolation at the cost of blurring, jagging and other artifacts due to errors in slope calculation. Non-linear methods, on the other hand, provide better edge preservation, but at the cost of high complexity and hence they can be considered very far from having real-time interpolation. The proposed method is a linear method that uses gradient orientation for slope calculation, unlike conventional linear methods that uses the contrast of nearby pixels. Prewitt edge detection is applied to separate uniform regions and edges. Simple line averaging is applied to unknown uniform regions, whereas unknown edge pixels are interpolated after calculation of slopes using gradient orientations of neighboring known edge pixels. As a post-processing step, bilateral filter is applied to interpolated edge regions in order to enhance the interpolated edges.

Keywords: edge detection, gradient orientation, image upscaling, linear interpolation, slope tracing

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Authors: K. N. S. Kasi Viswanadham

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Coupled system of second order linear and nonlinear boundary value problems occur in various fields of Science and Engineering. In the formulation of the problem, any one of 81 possible types of boundary conditions may occur. These 81 possible boundary conditions are written as a combination of four boundary conditions. To solve a coupled system of boundary value problem with these converted boundary conditions, a collocation method with cubic B-splines as basis functions has been developed. In the collocation method, the mesh points of the space variable domain have been selected as the collocation points. The basis functions have been redefined into a new set of basis functions which in number match with the number of mesh points in the space variable domain. The solution of a non-linear boundary value problem has been obtained as the limit of a sequence of solutions of linear boundary value problems generated by quasilinearization technique. Several linear and nonlinear boundary value problems are presented to test the efficiency of the proposed method and found that numerical results obtained by the present method are in good agreement with the exact solutions available in the literature.

Keywords: collocation method, coupled system, cubic b-splines, mesh points

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Authors: Boutahar Lhoucine, El Bikri Khalid, Benamar Rhali

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In this paper, the non-linear free axisymmetric vibration of a thin annular plate made of functionally graded material (FGM) has been studied by using the energy method and a multimode approach. FGM properties vary continuously as well as non-homogeneity through the thickness direction of the plate. The theoretical model is based on the classical plate theory and the Von Kármán geometrical non-linearity assumptions. An approximation has been adopted in the present work consisting of neglecting the in-plane deformation in the formulation. Hamilton’s principle is used to derive the governing equation of motion. The problem is solved by a numerical iterative procedure in order to obtain more accurate results for vibration amplitudes up to 1.5 times the plate thickness. The numerical results are given for the first axisymmetric non-linear mode shape for a wide range of vibration amplitudes and they are presented either in tabular form or in graphical form to show the effect that the vibration amplitude and the variation in material properties have significant effects on the frequencies and the bending stresses in large amplitude vibration of the functionally graded annular plate.

Keywords: non-linear vibrations, annular plates, large amplitudes, functionally graded material

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Authors: Fatemeh Nemati, Lucinda Leonard, Gwyn Lintern, Richard Thomson

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In this study, we will use modern numerical modeling approaches to estimate tsunami risks to the southern coast of British Columbia from landslides. Wave generation is to be simulated using the NHWAVE model, which solves the Navier-Stokes equations due to the more complex behavior of flow near the landslide source; far-field wave propagation will be simulated using the simpler model FUNWAVE_TVD with high-order Boussinesq-type wave equations, with a focus on the accurate simulation of wave propagation and regional- or coastal-scale inundation predictions.

Keywords: FUNWAVE-TVD, landslide-generated tsunami, NHWAVE, tsunami risk

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Authors: Intan Maisarah Abd Rahim, Herlina Abdul Rahim, Rashidah Ghazali

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Diabetes is a medical condition that can lead to various diseases such as stroke, heart disease, blindness and obesity. In clinical practice, the concern of the diabetic patients towards the blood glucose examination is rather alarming as some of the individual describing it as something painful with pinprick and pinch. As for some patient with high level of glucose level, pricking the fingers multiple times a day with the conventional glucose meter for close monitoring can be tiresome, time consuming and painful. With these concerns, several non-invasive techniques were used by researchers in measuring the glucose level in blood, including ultrasonic sensor implementation, multisensory systems, absorbance of transmittance, bio-impedance, voltage intensity, and thermography. This paper is discussing the application of the near-infrared (NIR) spectroscopy as a non-invasive method in measuring the glucose level and the implementation of the linear system identification model in predicting the output data for the NIR measurement. In this study, the wavelengths considered are at the 1450 nm and 1950 nm. Both of these wavelengths showed the most reliable information on the glucose presence in blood. Then, the linear Autoregressive Moving Average Exogenous model (ARMAX) model with both un-regularized and regularized methods was implemented in predicting the output result for the NIR measurement in order to investigate the practicality of the linear system in this study. However, the result showed only 50.11% accuracy obtained from the system which is far from the satisfying results that should be obtained.

Keywords: diabetes, glucose level, linear, near-infrared, non-invasive, prediction system

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Authors: Tahmidul Islam

Abstract:

Propensity Score Matching (PSM) technique has been widely used for estimating causal effect of treatment in observational studies. One major step of implementing PSM is estimating the propensity score (PS). Logistic regression model with additive linear terms of covariates is most used technique in many studies. Logistics regression model is also used with cubic splines for retaining flexibility in the model. However, choosing the functional form of the logistic regression model has been a question since the effectiveness of PSM depends on how accurately the PS been estimated. In many situations, the linearity assumption of linear logistic regression may not hold and non-linear relation between the logit and the covariates may be appropriate. One can estimate PS using machine learning techniques such as random forest, neural network etc for more accuracy in non-linear situation. In this study, an attempt has been made to compare the efficacy of Generalized Additive Model (GAM) in various linear and non-linear settings and compare its performance with usual logistic regression. GAM is a non-parametric technique where functional form of the covariates can be unspecified and a flexible regression model can be fitted. In this study various simple and complex models have been considered for treatment under several situations (small/large sample, low/high number of treatment units) and examined which method leads to more covariate balance in the matched dataset. It is found that logistic regression model is impressively robust against inclusion quadratic and interaction terms and reduces mean difference in treatment and control set equally efficiently as GAM does. GAM provided no significantly better covariate balance than logistic regression in both simple and complex models. The analysis also suggests that larger proportion of controls than treatment units leads to better balance for both of the methods.

Keywords: accuracy, covariate balances, generalized additive model, logistic regression, non-linearity, propensity score matching

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Authors: Saghar Heidari

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In this paper, we study the valuation problem of European continuous-installment options under Markov-modulated models with a partial differential equation approach. Due to the opportunity for continuing or stopping to pay installments, the valuation problem under regime-switching models can be formulated as coupled partial differential equations (CPDE) with free boundary features. To value the installment options, we express the truncated CPDE as a linear complementarity problem (LCP), then a finite element method is proposed to solve the resulted variational inequality. Under some appropriate assumptions, we establish the stability of the method and illustrate some numerical results to examine the rate of convergence and accuracy of the proposed method for the pricing problem under the regime-switching model.

Keywords: continuous-installment option, European option, regime-switching model, finite element method

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Authors: Chahid K. Ghaddar

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The spreadsheet engine is exploited via a non-conventional mechanism to enable novel worksheet solver functions for computational calculus. The solver functions bypass inherent restrictions on built-in math and user defined functions by taking variable formulas as a new type of argument while retaining purity and recursion properties. The enabling mechanism permits integration of numerical algorithms into worksheet functions for solving virtually any computational problem that can be modelled by formulas and variables. Several examples are presented for computing integrals, derivatives, and systems of deferential-algebraic equations. Incorporation of the worksheet solver functions with the ubiquitous spreadsheet extend the utility of the latter as a powerful tool for computational mathematics.

Keywords: calculus, differential algebraic equations, solvers, spreadsheet

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Authors: Abdullah Eqal Al Mazrooei

Abstract:

Kalman filter is a famous algorithm that utilizes to estimate the state in the linear systems. It has numerous applications in technology and science. Since of the most of applications in real life can be described by nonlinear systems. So, Kalman filter does not work with the nonlinear systems because it is suitable to linear systems only. In this work, a nonlinear filtering algorithm is presented which is suitable to use with the special kinds of nonlinear systems. This filter generalizes the Kalman filter. This means that this filter also can be used for the linear systems. Our algorithm depends on a special linearization of the second degree. We introduced the nonlinear algorithm with a bilinear state-space model. A simulation example is presented to illustrate the efficiency of the algorithm.

Keywords: Kalman filter, filtering algorithm, nonlinear systems, state-space model

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Authors: Alireza Rafie Boldaji, Ahmad Saboonchi

Abstract:

Chokes are commonly used in oil and gas production systems. A choke is a restriction basically designed to control flow rates of oil and gas wells, to prevent the downstream disturbances from propagating upstream (critical flow), and to protect the surface equipment facilities against slugging at high flowing pressures. There are different methods to calculate the multiphase flow rate, one of the multiphase flow measurement methods is the separation and measurement by on¬e-phaseFlow meter, another common method is the use of movable separator, their operations are very labor-intensive and costly. The current method used is based on the flow differential pressure on both sides of choke. Three groups of correlations describing two-phase flow through wellhead chokes were examined. The first group involved simple empirical equations similar to those of Gilbert, the second group comprised derived equations of two-phase flow incorporating PVT properties, and third group is computational method. In the article we calculate the flow of oil and gas through choke with simulation of this two phase flow bye computational fluid dynamic method, we use Ansys- fluent for this simulation and finally compared results of computational simulation whit empirical equations, the results show good agreement between experimental and numerical results.

Keywords: CFD, two-phase, choke, critical

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Authors: Hassan Youssef Mohamed

Abstract:

In this paper, we show new wave equations, and by using the equations, we concluded that the strong force and the weak force are not fundamental, but they are quantum effects for electromagnetism. This result is different from the current scientific understanding about strong and weak interactions at all. So, we introduce three evidences for our theory. First, we prove the asymptotic freedom phenomenon in the strong force by using our model. Second, we derive the nuclear shell model as an approximation of our model. Third, we prove that the leptons do not participate in the strong interactions, and we prove the short ranges of weak and strong interactions. So, our model is consistent with the current understanding of physics. Finally, we introduce the electron-positron model as the basic ingredients for protons, neutrons, and all matters, so we can study all particles interactions and nuclear interaction as many-body problems of electrons and positrons. Also, we prove the violation of parity conservation in weak interaction as evidence of our theory in the weak interaction. Also, we calculate the average of the binding energy per nucleon.

Keywords: new wave equations, the strong force, the grand unification theory, hydrogen atom, weak force, the nuclear shell model, the asymptotic freedom, electron-positron model, the violation of parity conservation, the binding energy

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Authors: Tomyslav Sledevič, Artūras Serackis, Gintautas Tamulevičius, Dalius Navakauskas

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This paper presents a comparative evaluation of features extraction algorithm for a real-time isolated word recognition system based on FPGA. The Mel-frequency cepstral, linear frequency cepstral, linear predictive and their cepstral coefficients were implemented in hardware/software design. The proposed system was investigated in the speaker-dependent mode for 100 different Lithuanian words. The robustness of features extraction algorithms was tested recognizing the speech records at different signals to noise rates. The experiments on clean records show highest accuracy for Mel-frequency cepstral and linear frequency cepstral coefficients. For records with 15 dB signal to noise rate the linear predictive cepstral coefficients give best result. The hard and soft part of the system is clocked on 50 MHz and 100 MHz accordingly. For the classification purpose, the pipelined dynamic time warping core was implemented. The proposed word recognition system satisfies the real-time requirements and is suitable for applications in embedded systems.

Keywords: isolated word recognition, features extraction, MFCC, LFCC, LPCC, LPC, FPGA, DTW

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Authors: Tomoaki Hashimoto

Abstract:

Model predictive control is a kind of optimal feedback control in which control performance over a finite future is optimized with a performance index that has a moving initial time and a moving terminal time. This paper examines the stability of model predictive control for linear discrete-time systems with additive stochastic disturbances. A sufficient condition for the stability of the closed-loop system with model predictive control is derived by means of a linear matrix inequality. The objective of this paper is to show the results of computational simulations in order to verify the validity of the obtained stability condition.

Keywords: computational simulations, optimal control, predictive control, stochastic systems, discrete-time systems

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Authors: Tomoaki Hashimoto

Abstract:

Recently, feedback control systems using random dither quantizers have been proposed for linear discrete-time systems. However, the constraints imposed on state and control variables have not yet been taken into account for the design of feedback control systems with random dither quantization. Model predictive control is a kind of optimal feedback control in which control performance over a finite future is optimized with a performance index that has a moving initial and terminal time. An important advantage of model predictive control is its ability to handle constraints imposed on state and control variables. Based on the model predictive control approach, the objective of this paper is to present a control method that satisfies probabilistic state constraints for linear discrete-time feedback control systems with random dither quantization. In other words, this paper provides a method for solving the optimal control problems subject to probabilistic state constraints for linear discrete-time feedback control systems with random dither quantization.

Keywords: optimal control, stochastic systems, random dither, quantization

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Authors: A. A. James, A. O. Adesanya, M. R. Odekunle, D. G. Yakubu

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This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods.

Keywords: interpolation, approximate solution, collocation, differential system, half step, converges, block method, efficiency

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