Sie Long Kek | Universiti Tun Hussein Onn Malaysia (original) (raw)

Papers by Sie Long Kek

Research paper thumbnail of Curve Tracking of Nonlinear Dynamic System Using Linear State-Space Model

Proceedings of the International Conference of Control, Dynamic systems, and Robotics, Jun 1, 2024

In this paper, curve tracking of nonlinear dynamic systems is discussed. In mathematical modellin... more In this paper, curve tracking of nonlinear dynamic systems is discussed. In mathematical modelling, a curve is defined as the solution of a dynamic system. Assuming the actual model of a dynamic system is unknown, we only have the solution curve of a system. Hence, tracking the curve becomes prominent in studying a nonlinear dynamic system. For this purpose, we propose a linear state-space model to track the curve of a nonlinear dynamic system. First, a least squares optimization problem is introduced, where the differences between the system and the linear model are defined. An adaptive parameter is introduced in the linear model, aiming to capture these differences. Second, the first-order necessary condition is derived, and the adaptive parameter is determined to update the curve of the linear model. Once convergence is achieved, the optimal solution curve of the linear model approximates the correct solution curve of the nonlinear system despite model-reality differences. Third, an example of a chemical kinetics system is studied for illustration. The simulation results show the efficiency of the computation algorithm, and the iterative solution demonstrates the accuracy of curve tracking. Therefore, using the linear state-space model to track the curve of the nonlinear dynamic system is satisfactorily handled.

Research paper thumbnail of Standard Error Adaptive Moment Estimation for Mean-Value-at-Risk Portfolio Optimization Problems by Sampling

Vietnam journal of mathematics, Apr 1, 2024

In this paper, an improvement of the adaptive moment estimation (Adam) method equipped with stand... more In this paper, an improvement of the adaptive moment estimation (Adam) method equipped with standard error (SE), namely the AdamSE algorithm, is proposed. Our aims are to improve the convergence rate of the Adam algorithm and to explore the utility of the AdamSE algorithm for solving mean-value-at-risk (mean-VaR) portfolio optimization problems. For this, 10 stocks from the top 30 equity holdings list released by the Employees Provident Fund (EPF) have a weak correlation among them. The weekly stock prices of these stocks are selected for the period from 2015 to 2019, and then the mean, covariance and required rate of return are calculated to build a mean-VaR portfolio optimization model. In this way, the Adam and AdamSE algorithms are used to solve the model, and their results are compared. During the calculation, the stochastic gradients of the model are simulated through sampling, and nine samples are taken into consideration. With this sampling, the standard error of each sample is computed and the optimal weight for each sample is determined using the AdamSE algorithm. After convergence is achieved, the results show that different sample sizes could provide a satisfactory outcome for the portfolio concerned and from these nine samples, the lowest and highest iteration numbers were obtained to guarantee a robust optimal solution to the model constructed. Hence, we concluded that the AdamSE algorithm through sampling reveals its computational capability for handling the mean-VaR portfolio optimization problem. We dedicate this research article to members and postgraduate students in our research group. This is to encourage them to continue mathematical research works in optimization. We appreciate Prof. Dr. Hoang Xuan Phu's invitation to contribute the article to this special issue dedicated to Prof. Dr. Tamás Terlaky on his birthday.

Research paper thumbnail of Conjugate Gradient Approach for Linear Optimal Control of Damped Harmonic Oscillator

In this paper, applying the conjugate gradient method to solve the linear optimal control problem... more In this paper, applying the conjugate gradient method to solve the linear optimal control problem is discussed. In the optimization theory, the conjugate gradient method is an efficient computational approach for solving the unconstrained optimization problem, specifically, for quadratic case. Since the linear optimal control problem consists of the quadratic cost function and the linear dynamical system, the practical application of the conjugate gradient method to this kind of problem would be addressed. In our study, the necessary conditions for optimality for the linear optimal control problem are highlighted. Then, the equivalent optimization problem is formulated and the gradient function, which is given by the stationary condition, is evaluated. On this basis, the search direction, which satisfies the conjugacy, is determined definitely. During the iterative procedure, the control sequence is calculated such that the state sequence could be obtained. Once the convergence is achieved, the optimal solution of the linear optimal control problem is obtained. For illustration, the optimal control of damped harmonic oscillator is discussed. The results obtained show the efficiency of the approach used. In conclusion, the application of the conjugate gradient method to linear optimal control problem of the damped harmonic oscillator is highly presented.

Research paper thumbnail of Conjugate Gradient Approach for Optimal Control Problem with Model-Reality Differences

The 8th International Conference on Computational Methods (ICCM2017), Jun 19, 2017

In this paper, an efficient computation approach is proposed for solving a general class of optim... more In this paper, an efficient computation approach is proposed for solving a general class of optimal control problems. In our approach, a simplified model-based optimal control model, which is adding the adjusted parameters into the model used, is solved iteratively. In such a way, the differences between the real plant and the model used can be calculated, in turn, to update the optimal solution of the model used. During the computation procedure, the equivalent optimization problem is formulated, where the conjugate gradient algorithm is applied in solving the optimization problem. On this basis, the optimal solution of the modified model-based optimal control problem could be obtained repeatedly. Once the convergence is achieved, the iterative solution approximates to the correct optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, both linear and nonlinear examples are demonstrated to show the performance of the approach proposed. In conclusion, the efficiency of the approach proposed is highly presented.

Research paper thumbnail of Smoothing Solution for Discrete-Time Nonlinear Stochastic Optimal Control Problem with Model-Reality Differences

InTech eBooks, Oct 19, 2016

Research paper thumbnail of Testing of linear models for optimal control of second-order dynamical system based on model-reality differences

Results in control and optimization, Sep 1, 2021

In this paper, the testing of linear models with different parameter values is conducted for solv... more In this paper, the testing of linear models with different parameter values is conducted for solving the optimal control problem of a second-order dynamical system. The purpose of this testing is to provide the solution with the same structure but different parameter values in the model used. For doing so, the adjusted parameters are added to each model in order to measure the differences between the model used and the plant dynamics. On this basis, an expanded optimal control problem, which combines system optimization and parameter estimation, is introduced. Then, the Hamiltonian function is defined and a set of the necessary conditions is derived. Consequently, a modified model-based optimal control problem has resulted. Follow from this, an equivalent optimization problem without constraints is formulated. During the calculation procedure, the conjugate gradient algorithm is employed to solve the optimization problem, in turn, to update the adjusted parameters repeatedly for obtaining the optimal solution of the model used. Within a given tolerance, the iterative solution of the model used approximates the correct optimal solution of the original linear optimal control problem despite model-reality differences. The results obtained show the applicability of models with the same structures and different parameter values for solving the original linear optimal control problem. In conclusion, the efficiency of the approach proposed is highly verified.

Research paper thumbnail of The Performance of K-Means and K-Modes Clustering to Identify Cluster in Numerical Data

Journal of Science and Technology, Dec 26, 2017

Cluster analysis is a formal study of methods and algorithms for natural grouping of objects acco... more Cluster analysis is a formal study of methods and algorithms for natural grouping of objects according to the perceived intrinsic characteristics and the measure similarities in each group of the objects. The pattern of each cluster and the relationship for each cluster are identified, then they are related to the frequency of occurrence in the data set. Meanwhile, the mean and the mode are known as the measures of central tendency in a distribution. In clustering, the mean and the mode are applied as a technique to discover the existing of the cluster in the data set. Therefore, this study aims to compare the performance of K-means and K-modes clustering techniques in finding the group of cluster that exists in the numerical data. The difference between these methods is that the K-modes method is usually applied to categorical data, while K-means method is applied to numerical data. However, both methods would be used to cluster the numerical data in this study. Moreover, performance of these two clustering methods are demonstrated using the output from R software. The results obtained are compared such that the method giving the best output could be determined. In conclusion, the efficiency of the methods is highly presented.

Research paper thumbnail of Optimal control of a coupled tanks system with model-reality differences

Nucleation and Atmospheric Aerosols, 2017

In this paper, an efficient computational approach is proposed to optimize and control a coupled ... more In this paper, an efficient computational approach is proposed to optimize and control a coupled tanks system. Since the dynamics of the coupled tanks system is nonlinear, determination of the optimal water level in the tanks could be formulated as an optimal control problem for a useful operation decision. For simplicity, the linear model of the coupled tanks system is suggested to give the true operating height of the coupled tanks. In our approach, the adjustable parameter is added into the model used. The aim is to measure the differences between the real plant and the model used repeatedly during the computation procedure. In this way, the optimal solution of the model used can be updated iteratively. On this basis, system optimization and parameter estimation are integrated. At the end of the iteration procedure, the converged solution approximates to the correct optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, the numerical parameters of a coupled tank system are studied and the applicable of the approach proposed is shown. In conclusion, the efficiency of the approach proposed in achieving the desired water level of the coupled tanks is highly presented.

Research paper thumbnail of Analysis of survival in breast cancer patients by using different parametric models

Journal of physics, Sep 1, 2017

View the article online for updates and enhancements. Related content Methodology to predict a ma... more View the article online for updates and enhancements. Related content Methodology to predict a maximum followup period for breast cancer patients Richard F Mould, Bernard Asselain and Yann De Rycke-Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

Research paper thumbnail of An integrated optimal control algorithm for discrete-time nonlinear stochastic system

International Journal of Control, Dec 1, 2010

ABSTRACT Consider a discrete-time nonlinear system with random disturbances appearing in the real... more ABSTRACT Consider a discrete-time nonlinear system with random disturbances appearing in the real plant and the output channel where the randomly perturbed output is measurable. An iterative procedure based on the linear quadratic Gaussian optimal control model is developed for solving the optimal control of this stochastic system. The optimal state estimate provided by Kalman filtering theory and the optimal control law obtained from the linear quadratic regulator problem are then integrated into the dynamic integrated system optimisation and parameter estimation algorithm. The iterative solutions of the optimal control problem for the model obtained converge to the solution of the original optimal control problem of the discrete-time nonlinear system, despite model-reality differences, when the convergence is achieved. An illustrative example is solved using the method proposed. The results obtained show the effectiveness of the algorithm proposed.

Research paper thumbnail of Exam Marks Summation App Using Tesseract OCR in Python

International Journal of Integrated Engineering, Jun 20, 2022

Research paper thumbnail of Power Factor Improvement in Power System with the Integration of Renewable Energy

Journal of Telecommunication, Electronic and Computer Engineering, Mar 1, 2018

Research paper thumbnail of An Expanded Optimal Control Policy for a Coupled Tanks System with Random Disturbance

Advances in Pure Mathematics, 2019

In this paper, an expanded optimal control policy is proposed to study the coupled tanks system, ... more In this paper, an expanded optimal control policy is proposed to study the coupled tanks system, where the random disturbance is added into the system. Since the dynamics of the coupled tanks system can be formulated as a nonlinear system, determination of the optimal water level in the tanks is useful for the operation decision. On this point of view, the coupled tanks system dynamics is usually linearized to give the steady state operating height. In our approach, a model-based optimal control problem, which is adding with adjusted parameters, is considered to obtain the true operating height of the real coupled tanks system. During the computation procedure, the differences between the real plant and the model used are measured repeatedly, where the optimal solution of the model used is updated. On this basis, system optimization and parameter estimation are integrated. At the end of the iteration, the iterative solution approximates to the correct optimal solution of the original optimal control problem, in spite of model-reality differences. In conclusion, the efficiency of the approach proposed is shown.

Research paper thumbnail of Stochastic Optimal Control of Economic Growth Model under Research and Development Investment with Kalman Filtering Approaches

Journal of Hunan University Natural Sciences, Jun 30, 2022

Research paper thumbnail of A simulation optimization model for portfolio selection problem with quadratic programming technique

PROCEEDINGS OF INTERNATIONAL CONFERENCE ON ADVANCES IN MATERIALS RESEARCH (ICAMR - 2019), 2020

Research paper thumbnail of Conjugate Gradient Approach for Discrete Time Optimal Control Problems with Model-Reality Differences

IntechOpen eBooks, Nov 22, 2019

Research paper thumbnail of A Gauss-Newton Approach for Nonlinear Optimal Control Problem with Model-Reality Differences

Open journal of optimization, 2017

Output measurement for nonlinear optimal control problems is an interesting issue. Because the st... more Output measurement for nonlinear optimal control problems is an interesting issue. Because the structure of the real plant is complex, the output channel could give a significant response corresponding to the real plant. In this paper, a least squares scheme, which is based on the Gauss-Newton algorithm, is proposed. The aim is to approximate the output that is measured from the real plant. In doing so, an appropriate output measurement from the model used is suggested. During the computation procedure, the control trajectory is updated iteratively by using the Gauss-Newton recursion scheme. Consequently, the output residual between the original output and the suggested output is minimized. Here, the linear model-based optimal control model is considered, so as the optimal control law is constructed. By feed backing the updated control trajectory into the dynamic system, the iterative solution of the model used could approximate to the correct optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, current converted and isothermal reaction rector problems are studied and the results are demonstrated. In conclusion, the efficiency of the approach proposed is highly presented.

Research paper thumbnail of A gradient algorithm for optimal control problems with model-reality differences

Numerical Algebra, Control and Optimization, 2015

In this paper, we propose a computational approach to solve a model-based optimal control problem... more In this paper, we propose a computational approach to solve a model-based optimal control problem. Our aim is to obtain the optimal solution of the nonlinear optimal control problem. Since the structures of both problems are different, only solving the model-based optimal control problem will not give the optimal solution of the nonlinear optimal control problem. In our approach, the adjusted parameters are added into the model used so as the differences between the real plant and the model can be measured. On this basis, an expanded optimal control problem is introduced, where system optimization and parameter estimation are integrated interactively. The Hamiltonian function, which adjoins the cost function, the state equation and the additional constraints, is defined. By applying the calculus of variation, a set of the necessary optimality conditions, which defines modified model-based optimal control problem, parameter estimation problem and computation of modifiers, is then derived. To obtain the optimal solution, the modified modelbased optimal control problem is converted in a nonlinear programming problem through the canonical formulation, where the gradient formulation can be made. During the iterative procedure, the control sequences are generated as the admissible control law of the model used, together with the corresponding state sequences. Consequently, the optimal solution is updated repeatedly by the adjusted parameters. At the end of iteration, the converged solution approaches to the correct optimal solution of the original optimal control problem in spite of model-reality differences. For illustration, two examples are studied and the results show the efficiency of the approach proposed.

Research paper thumbnail of Efficient Output Solution for Nonlinear Stochastic Optimal Control Problem with Model-Reality Differences

Mathematical Problems in Engineering, 2015

A computational approach is proposed for solving the discrete time nonlinear stochastic optimal c... more A computational approach is proposed for solving the discrete time nonlinear stochastic optimal control problem. Our aim is to obtain the optimal output solution of the original optimal control problem through solving the simplified model-based optimal control problem iteratively. In our approach, the adjusted parameters are introduced into the model used such that the differences between the real system and the model used can be computed. Particularly, system optimization and parameter estimation are integrated interactively. On the other hand, the output is measured from the real plant and is fed back into the parameter estimation problem to establish a matching scheme. During the calculation procedure, the iterative solution is updated in order to approximate the true optimal solution of the original optimal control problem despite model-reality differences. For illustration, a wastewater treatment problem is studied and the results show the efficiency of the approach proposed.

Research paper thumbnail of State estimation and optimal control of an inverted pendulum on a cart system with stochastic approximation approach

In this paper, optimal control of an inverted pendulum on a cart system is studied. Since the non... more In this paper, optimal control of an inverted pendulum on a cart system is studied. Since the nonlinear structure of the system is complex, and in the presence of random disturbances, optimization and control of the motion of the system become more challenging. For handling this system, a discrete-time stochastic optimal control problem for the system is described, where the external force is considered as the control input. By defining a loss function, namely, the mean squared errors to be minimized, the stochastic approximation (SA) approach is applied to estimate the state dynamics. In addition, the Hamiltonian function is defined, and the first-order necessary conditions are derived. The gradient of the cost function is determined so that the SA approach is employed to update the control sequences. For illustration, considering the values of the related parameters in the system, the discrete-time stochastic optimal control problem is solved iteratively by using the SA algorithm. The simulation results show that the state estimation and the optimal control law design are well performed with the SA algorithm, and the motion of the inverted pendulum cart is addressed satisfactorily. In conclusion, the efficiency of the SA approach for solving the inverted pendulum on a cart system is verified.

Research paper thumbnail of Curve Tracking of Nonlinear Dynamic System Using Linear State-Space Model

Proceedings of the International Conference of Control, Dynamic systems, and Robotics, Jun 1, 2024

In this paper, curve tracking of nonlinear dynamic systems is discussed. In mathematical modellin... more In this paper, curve tracking of nonlinear dynamic systems is discussed. In mathematical modelling, a curve is defined as the solution of a dynamic system. Assuming the actual model of a dynamic system is unknown, we only have the solution curve of a system. Hence, tracking the curve becomes prominent in studying a nonlinear dynamic system. For this purpose, we propose a linear state-space model to track the curve of a nonlinear dynamic system. First, a least squares optimization problem is introduced, where the differences between the system and the linear model are defined. An adaptive parameter is introduced in the linear model, aiming to capture these differences. Second, the first-order necessary condition is derived, and the adaptive parameter is determined to update the curve of the linear model. Once convergence is achieved, the optimal solution curve of the linear model approximates the correct solution curve of the nonlinear system despite model-reality differences. Third, an example of a chemical kinetics system is studied for illustration. The simulation results show the efficiency of the computation algorithm, and the iterative solution demonstrates the accuracy of curve tracking. Therefore, using the linear state-space model to track the curve of the nonlinear dynamic system is satisfactorily handled.

Research paper thumbnail of Standard Error Adaptive Moment Estimation for Mean-Value-at-Risk Portfolio Optimization Problems by Sampling

Vietnam journal of mathematics, Apr 1, 2024

In this paper, an improvement of the adaptive moment estimation (Adam) method equipped with stand... more In this paper, an improvement of the adaptive moment estimation (Adam) method equipped with standard error (SE), namely the AdamSE algorithm, is proposed. Our aims are to improve the convergence rate of the Adam algorithm and to explore the utility of the AdamSE algorithm for solving mean-value-at-risk (mean-VaR) portfolio optimization problems. For this, 10 stocks from the top 30 equity holdings list released by the Employees Provident Fund (EPF) have a weak correlation among them. The weekly stock prices of these stocks are selected for the period from 2015 to 2019, and then the mean, covariance and required rate of return are calculated to build a mean-VaR portfolio optimization model. In this way, the Adam and AdamSE algorithms are used to solve the model, and their results are compared. During the calculation, the stochastic gradients of the model are simulated through sampling, and nine samples are taken into consideration. With this sampling, the standard error of each sample is computed and the optimal weight for each sample is determined using the AdamSE algorithm. After convergence is achieved, the results show that different sample sizes could provide a satisfactory outcome for the portfolio concerned and from these nine samples, the lowest and highest iteration numbers were obtained to guarantee a robust optimal solution to the model constructed. Hence, we concluded that the AdamSE algorithm through sampling reveals its computational capability for handling the mean-VaR portfolio optimization problem. We dedicate this research article to members and postgraduate students in our research group. This is to encourage them to continue mathematical research works in optimization. We appreciate Prof. Dr. Hoang Xuan Phu's invitation to contribute the article to this special issue dedicated to Prof. Dr. Tamás Terlaky on his birthday.

Research paper thumbnail of Conjugate Gradient Approach for Linear Optimal Control of Damped Harmonic Oscillator

In this paper, applying the conjugate gradient method to solve the linear optimal control problem... more In this paper, applying the conjugate gradient method to solve the linear optimal control problem is discussed. In the optimization theory, the conjugate gradient method is an efficient computational approach for solving the unconstrained optimization problem, specifically, for quadratic case. Since the linear optimal control problem consists of the quadratic cost function and the linear dynamical system, the practical application of the conjugate gradient method to this kind of problem would be addressed. In our study, the necessary conditions for optimality for the linear optimal control problem are highlighted. Then, the equivalent optimization problem is formulated and the gradient function, which is given by the stationary condition, is evaluated. On this basis, the search direction, which satisfies the conjugacy, is determined definitely. During the iterative procedure, the control sequence is calculated such that the state sequence could be obtained. Once the convergence is achieved, the optimal solution of the linear optimal control problem is obtained. For illustration, the optimal control of damped harmonic oscillator is discussed. The results obtained show the efficiency of the approach used. In conclusion, the application of the conjugate gradient method to linear optimal control problem of the damped harmonic oscillator is highly presented.

Research paper thumbnail of Conjugate Gradient Approach for Optimal Control Problem with Model-Reality Differences

The 8th International Conference on Computational Methods (ICCM2017), Jun 19, 2017

In this paper, an efficient computation approach is proposed for solving a general class of optim... more In this paper, an efficient computation approach is proposed for solving a general class of optimal control problems. In our approach, a simplified model-based optimal control model, which is adding the adjusted parameters into the model used, is solved iteratively. In such a way, the differences between the real plant and the model used can be calculated, in turn, to update the optimal solution of the model used. During the computation procedure, the equivalent optimization problem is formulated, where the conjugate gradient algorithm is applied in solving the optimization problem. On this basis, the optimal solution of the modified model-based optimal control problem could be obtained repeatedly. Once the convergence is achieved, the iterative solution approximates to the correct optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, both linear and nonlinear examples are demonstrated to show the performance of the approach proposed. In conclusion, the efficiency of the approach proposed is highly presented.

Research paper thumbnail of Smoothing Solution for Discrete-Time Nonlinear Stochastic Optimal Control Problem with Model-Reality Differences

InTech eBooks, Oct 19, 2016

Research paper thumbnail of Testing of linear models for optimal control of second-order dynamical system based on model-reality differences

Results in control and optimization, Sep 1, 2021

In this paper, the testing of linear models with different parameter values is conducted for solv... more In this paper, the testing of linear models with different parameter values is conducted for solving the optimal control problem of a second-order dynamical system. The purpose of this testing is to provide the solution with the same structure but different parameter values in the model used. For doing so, the adjusted parameters are added to each model in order to measure the differences between the model used and the plant dynamics. On this basis, an expanded optimal control problem, which combines system optimization and parameter estimation, is introduced. Then, the Hamiltonian function is defined and a set of the necessary conditions is derived. Consequently, a modified model-based optimal control problem has resulted. Follow from this, an equivalent optimization problem without constraints is formulated. During the calculation procedure, the conjugate gradient algorithm is employed to solve the optimization problem, in turn, to update the adjusted parameters repeatedly for obtaining the optimal solution of the model used. Within a given tolerance, the iterative solution of the model used approximates the correct optimal solution of the original linear optimal control problem despite model-reality differences. The results obtained show the applicability of models with the same structures and different parameter values for solving the original linear optimal control problem. In conclusion, the efficiency of the approach proposed is highly verified.

Research paper thumbnail of The Performance of K-Means and K-Modes Clustering to Identify Cluster in Numerical Data

Journal of Science and Technology, Dec 26, 2017

Cluster analysis is a formal study of methods and algorithms for natural grouping of objects acco... more Cluster analysis is a formal study of methods and algorithms for natural grouping of objects according to the perceived intrinsic characteristics and the measure similarities in each group of the objects. The pattern of each cluster and the relationship for each cluster are identified, then they are related to the frequency of occurrence in the data set. Meanwhile, the mean and the mode are known as the measures of central tendency in a distribution. In clustering, the mean and the mode are applied as a technique to discover the existing of the cluster in the data set. Therefore, this study aims to compare the performance of K-means and K-modes clustering techniques in finding the group of cluster that exists in the numerical data. The difference between these methods is that the K-modes method is usually applied to categorical data, while K-means method is applied to numerical data. However, both methods would be used to cluster the numerical data in this study. Moreover, performance of these two clustering methods are demonstrated using the output from R software. The results obtained are compared such that the method giving the best output could be determined. In conclusion, the efficiency of the methods is highly presented.

Research paper thumbnail of Optimal control of a coupled tanks system with model-reality differences

Nucleation and Atmospheric Aerosols, 2017

In this paper, an efficient computational approach is proposed to optimize and control a coupled ... more In this paper, an efficient computational approach is proposed to optimize and control a coupled tanks system. Since the dynamics of the coupled tanks system is nonlinear, determination of the optimal water level in the tanks could be formulated as an optimal control problem for a useful operation decision. For simplicity, the linear model of the coupled tanks system is suggested to give the true operating height of the coupled tanks. In our approach, the adjustable parameter is added into the model used. The aim is to measure the differences between the real plant and the model used repeatedly during the computation procedure. In this way, the optimal solution of the model used can be updated iteratively. On this basis, system optimization and parameter estimation are integrated. At the end of the iteration procedure, the converged solution approximates to the correct optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, the numerical parameters of a coupled tank system are studied and the applicable of the approach proposed is shown. In conclusion, the efficiency of the approach proposed in achieving the desired water level of the coupled tanks is highly presented.

Research paper thumbnail of Analysis of survival in breast cancer patients by using different parametric models

Journal of physics, Sep 1, 2017

View the article online for updates and enhancements. Related content Methodology to predict a ma... more View the article online for updates and enhancements. Related content Methodology to predict a maximum followup period for breast cancer patients Richard F Mould, Bernard Asselain and Yann De Rycke-Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

Research paper thumbnail of An integrated optimal control algorithm for discrete-time nonlinear stochastic system

International Journal of Control, Dec 1, 2010

ABSTRACT Consider a discrete-time nonlinear system with random disturbances appearing in the real... more ABSTRACT Consider a discrete-time nonlinear system with random disturbances appearing in the real plant and the output channel where the randomly perturbed output is measurable. An iterative procedure based on the linear quadratic Gaussian optimal control model is developed for solving the optimal control of this stochastic system. The optimal state estimate provided by Kalman filtering theory and the optimal control law obtained from the linear quadratic regulator problem are then integrated into the dynamic integrated system optimisation and parameter estimation algorithm. The iterative solutions of the optimal control problem for the model obtained converge to the solution of the original optimal control problem of the discrete-time nonlinear system, despite model-reality differences, when the convergence is achieved. An illustrative example is solved using the method proposed. The results obtained show the effectiveness of the algorithm proposed.

Research paper thumbnail of Exam Marks Summation App Using Tesseract OCR in Python

International Journal of Integrated Engineering, Jun 20, 2022

Research paper thumbnail of Power Factor Improvement in Power System with the Integration of Renewable Energy

Journal of Telecommunication, Electronic and Computer Engineering, Mar 1, 2018

Research paper thumbnail of An Expanded Optimal Control Policy for a Coupled Tanks System with Random Disturbance

Advances in Pure Mathematics, 2019

In this paper, an expanded optimal control policy is proposed to study the coupled tanks system, ... more In this paper, an expanded optimal control policy is proposed to study the coupled tanks system, where the random disturbance is added into the system. Since the dynamics of the coupled tanks system can be formulated as a nonlinear system, determination of the optimal water level in the tanks is useful for the operation decision. On this point of view, the coupled tanks system dynamics is usually linearized to give the steady state operating height. In our approach, a model-based optimal control problem, which is adding with adjusted parameters, is considered to obtain the true operating height of the real coupled tanks system. During the computation procedure, the differences between the real plant and the model used are measured repeatedly, where the optimal solution of the model used is updated. On this basis, system optimization and parameter estimation are integrated. At the end of the iteration, the iterative solution approximates to the correct optimal solution of the original optimal control problem, in spite of model-reality differences. In conclusion, the efficiency of the approach proposed is shown.

Research paper thumbnail of Stochastic Optimal Control of Economic Growth Model under Research and Development Investment with Kalman Filtering Approaches

Journal of Hunan University Natural Sciences, Jun 30, 2022

Research paper thumbnail of A simulation optimization model for portfolio selection problem with quadratic programming technique

PROCEEDINGS OF INTERNATIONAL CONFERENCE ON ADVANCES IN MATERIALS RESEARCH (ICAMR - 2019), 2020

Research paper thumbnail of Conjugate Gradient Approach for Discrete Time Optimal Control Problems with Model-Reality Differences

IntechOpen eBooks, Nov 22, 2019

Research paper thumbnail of A Gauss-Newton Approach for Nonlinear Optimal Control Problem with Model-Reality Differences

Open journal of optimization, 2017

Output measurement for nonlinear optimal control problems is an interesting issue. Because the st... more Output measurement for nonlinear optimal control problems is an interesting issue. Because the structure of the real plant is complex, the output channel could give a significant response corresponding to the real plant. In this paper, a least squares scheme, which is based on the Gauss-Newton algorithm, is proposed. The aim is to approximate the output that is measured from the real plant. In doing so, an appropriate output measurement from the model used is suggested. During the computation procedure, the control trajectory is updated iteratively by using the Gauss-Newton recursion scheme. Consequently, the output residual between the original output and the suggested output is minimized. Here, the linear model-based optimal control model is considered, so as the optimal control law is constructed. By feed backing the updated control trajectory into the dynamic system, the iterative solution of the model used could approximate to the correct optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, current converted and isothermal reaction rector problems are studied and the results are demonstrated. In conclusion, the efficiency of the approach proposed is highly presented.

Research paper thumbnail of A gradient algorithm for optimal control problems with model-reality differences

Numerical Algebra, Control and Optimization, 2015

In this paper, we propose a computational approach to solve a model-based optimal control problem... more In this paper, we propose a computational approach to solve a model-based optimal control problem. Our aim is to obtain the optimal solution of the nonlinear optimal control problem. Since the structures of both problems are different, only solving the model-based optimal control problem will not give the optimal solution of the nonlinear optimal control problem. In our approach, the adjusted parameters are added into the model used so as the differences between the real plant and the model can be measured. On this basis, an expanded optimal control problem is introduced, where system optimization and parameter estimation are integrated interactively. The Hamiltonian function, which adjoins the cost function, the state equation and the additional constraints, is defined. By applying the calculus of variation, a set of the necessary optimality conditions, which defines modified model-based optimal control problem, parameter estimation problem and computation of modifiers, is then derived. To obtain the optimal solution, the modified modelbased optimal control problem is converted in a nonlinear programming problem through the canonical formulation, where the gradient formulation can be made. During the iterative procedure, the control sequences are generated as the admissible control law of the model used, together with the corresponding state sequences. Consequently, the optimal solution is updated repeatedly by the adjusted parameters. At the end of iteration, the converged solution approaches to the correct optimal solution of the original optimal control problem in spite of model-reality differences. For illustration, two examples are studied and the results show the efficiency of the approach proposed.

Research paper thumbnail of Efficient Output Solution for Nonlinear Stochastic Optimal Control Problem with Model-Reality Differences

Mathematical Problems in Engineering, 2015

A computational approach is proposed for solving the discrete time nonlinear stochastic optimal c... more A computational approach is proposed for solving the discrete time nonlinear stochastic optimal control problem. Our aim is to obtain the optimal output solution of the original optimal control problem through solving the simplified model-based optimal control problem iteratively. In our approach, the adjusted parameters are introduced into the model used such that the differences between the real system and the model used can be computed. Particularly, system optimization and parameter estimation are integrated interactively. On the other hand, the output is measured from the real plant and is fed back into the parameter estimation problem to establish a matching scheme. During the calculation procedure, the iterative solution is updated in order to approximate the true optimal solution of the original optimal control problem despite model-reality differences. For illustration, a wastewater treatment problem is studied and the results show the efficiency of the approach proposed.

Research paper thumbnail of State estimation and optimal control of an inverted pendulum on a cart system with stochastic approximation approach

In this paper, optimal control of an inverted pendulum on a cart system is studied. Since the non... more In this paper, optimal control of an inverted pendulum on a cart system is studied. Since the nonlinear structure of the system is complex, and in the presence of random disturbances, optimization and control of the motion of the system become more challenging. For handling this system, a discrete-time stochastic optimal control problem for the system is described, where the external force is considered as the control input. By defining a loss function, namely, the mean squared errors to be minimized, the stochastic approximation (SA) approach is applied to estimate the state dynamics. In addition, the Hamiltonian function is defined, and the first-order necessary conditions are derived. The gradient of the cost function is determined so that the SA approach is employed to update the control sequences. For illustration, considering the values of the related parameters in the system, the discrete-time stochastic optimal control problem is solved iteratively by using the SA algorithm. The simulation results show that the state estimation and the optimal control law design are well performed with the SA algorithm, and the motion of the inverted pendulum cart is addressed satisfactorily. In conclusion, the efficiency of the SA approach for solving the inverted pendulum on a cart system is verified.

Research paper thumbnail of First-Order Linear Ordinary Differential Equation for Regression Modelling

Frontiers in Artificial Intelligence and Applications, 2024

This paper discusses the data-driven regression modelling using first-order linear ordinary diffe... more This paper discusses the data-driven regression modelling using first-order linear ordinary differential equation (ODE). First, we consider a set of actual data and calculate the numerical derivative. Then, a general equation for the first-order linear ODE is introduced. There are two parameters, namely the regression parameters, in the equation, and their value will be determined in regression modelling. After this, a loss function is defined as the sum of squared errors to minimize the differences between estimated and actual data. A set of necessary conditions is derived, and the regression parameters are analytically determined. Based on these optimal parameter estimates, the solution of the first-order linear ODE, which matches the actual data trend, shall be obtained. Finally, two financial examples, the sales volume of Proton cars and the housing index, are illustrated. Simulation results show that an appropriate first-order ODE model for these examples can be suggested. From our study, the practicality of using the first-order linear ODE for regression modelling is significantly demonstrated.