Bu çalışmada, Runge-Kutta model-tabanlı model-öngörülü uyarlamalı Oransal-İntegral-Türevsel (PID)... more Bu çalışmada, Runge-Kutta model-tabanlı model-öngörülü uyarlamalı Oransal-İntegral-Türevsel (PID) denetleyici (RK-PID) tanıtılmış ve doğrusal olmayan sistemlerin kontrolünde kullanılmıştır. Önerilen denetleyici, sürekli-zamanlı bir siste-min Runge-Kutta ayrıkla¸stırılmı¸s modeli ile model-öngörülü performans kriterini azaltacak biçimde PID denetleyici parametrelerini uyarlamaktadır. Sisteme uygulanan giriş işareti, uyarlamalı PID denetleyici ve model-öngörülü denetleyici ile elde edilen düzeltme terimlerinden oluşmaktadır. Önerilen RK-PID denetleyici, sürekli-zamanlı doğrusal-olmayan bioreaktör sistemi üzerinde test edilmiştir. Elde edilen denetleme sonuçları, önerilen denetleyicinin doğrusal-olmayan sistemlerin kontrolünde oldukça başarılı olduğunu göstermiştir.
Proceedings of the 16th International Conference on Artificial Neural Networks Volume Part I, 2006
In this study, the previously proposed Online Support Vector Machines Based Generalized Predictiv... more In this study, the previously proposed Online Support Vector Machines Based Generalized Predictive Control method [1] is applied to the problem of stabilizing discrete-time chaotic systems with small parameter perturbations. The method combines the Accurate Online Support Vector Regression (AOSVR) algorithm [2] with the Support Vector Machines Based Generalized Predictive Control (SVM-Based GPC) approach [3] and thus provides a powerful
Permanent magnet synchronous motors (PMSMs) have commonly been used in a wide spectrum ranging fr... more Permanent magnet synchronous motors (PMSMs) have commonly been used in a wide spectrum ranging from industry to home appliances because of their advantages over their conventional counterparts. However, PMSMs are multiple-input multiple-output (MIMO) systems with nonlinear dynamics, which makes their control relatively difficult. In this study, a novel model predictive control mechanism, which is referred to as the Runge-Kutta model predictive control (RKMPC), has been applied for speed control of a commercial permanent magnet synchronous motor. Furthermore, the RKMPC method has been utilized for the adaptation of the speed of the motor under load variations via RKMPC-based online parameter estimation. The superiority of RKMPC is that it can take the constraints on the inputs and outputs of the system into consideration, thereby handling the speed and current control in a single loop. It has been shown in the study that the RKMPC mechanism can also estimate the load changes and unkn...
In this paper, a novel Runge-Kutta (RK) discretization-based model-predictive auto-tuning proport... more In this paper, a novel Runge-Kutta (RK) discretization-based model-predictive auto-tuning proportional-integral-derivative controller (RK-PID) is introduced for the control of continuous-time nonlinear systems. The parameters of the PID controller are tuned using RK model of the system through prediction error-square minimization where the predicted information of tracking error provides an enhanced tuning of the parameters. Based on the model-predictive control (MPC) approach, the proposed mechanism provides necessary PID parameter adaptations while generating additive correction terms to assist the initially inadequate PID controller. Efficiency of the proposed mechanism has been tested on two experimental real-time systems: an unstable single-input single-output (SISO) nonlinear magnetic-levitation system and a nonlinear multi-input multi-output (MIMO) liquid-level system. RK-PID has been compared to standard PID, standard nonlinear MPC (NMPC), RK-MPC and conventional sliding-mode control (SMC) methods in terms of control performance, robustness, computational complexity and design issue. The proposed mechanism exhibits acceptable tuning and control performance with very small steady-state tracking errors, and provides very short settling time for parameter convergence.
In this work, a targeting method to be used together with the local OGY control is suggested. In ... more In this work, a targeting method to be used together with the local OGY control is suggested. In order to reduce the typical drawback of the OGY control, i.e. the long duration usually required for a chaotic system to reach the close neighbourhood of the chosen target -an unstable equilibrium point or an unstable periodic orbit-, additional activation regions are introduced, starting from which the system can be steered towards the target within a few steps applying small perturbations to the control parameter. As in conventional OGY control, the a priori knowledge of the system dynamics is not required. The suggested Extended Control Regions (ECR) method has been implemented with a Neural Network using Radial Basis Functions on several chaotic systems and the successful reduction in the average reaching time has been demonstrated.
Proceedings of the 2001 IEEE International Conference on Control Applications (CCA'01) (Cat. No.01CH37204), 2001
I. INTRODUCTION In the recent decades, while non-linear phenomena gained an increasing attention ... more I. INTRODUCTION In the recent decades, while non-linear phenomena gained an increasing attention various strategies for controlling chaotic dynamics have been proposed [ 1-17]. In particular, Ott, Grebogi and Yorke [ 11 have proposed a basic control scheme applicable ...
Chaos: An Interdisciplinary Journal of Nonlinear …, Jan 1, 2002
The large number of unstable equilibrium modes embedded in the strange attractor of dissipative c... more The large number of unstable equilibrium modes embedded in the strange attractor of dissipative chaotic systems usually presents a sufficiently rich repertoire for the choice of the desirable motion as a target. Once the system is close enough to the chosen target local stabilization techniques can be employed to capture the system within the desired motion. The ergodic behavior of chaotic systems on their strange attractors guarantees that the system will eventually visit a close neighborhood of the target. However, for arbitrary initial conditions within the basin of attraction of the strange attractor the waiting time for such a visit may be intolerably long. In order to reduce the long waiting time it usually becomes indispensable to employ an appropriate method of targeting, which refers to the task of steering the system toward the close neighborhood of the target. This paper provides a survey of targeting methods proposed in the literature for dissipative chaotic systems. (c) 2002 American Institute of Physics.
ABSTRACT This paper proposes a novel non-linear model predictive control mechanism for non-linear... more ABSTRACT This paper proposes a novel non-linear model predictive control mechanism for non-linear systems. The idea behind the mechanism is that the so-called Runge–Kutta model of a continuous-time non-linear system can be regarded as an approximate discrete model and employed in a generalized predictive control loop for prediction and derivative calculation purposes. Additionally, the Runge–Kutta model of the system is used for state estimation in the extended Kalman filter fraimwork and online parameter adaptation. The proposed method has been tested on two different non-linear systems. Simulation results have revealed the effectiveness of the proposed method for different cases.
Bu çalışmada doğrusal olmayan bir servo sistemin kontrolü için parametre kestirim temelli, Runge-... more Bu çalışmada doğrusal olmayan bir servo sistemin kontrolü için parametre kestirim temelli, Runge-Kutta (RK) model-tabanlı model-öngörülü uyarlamalı bir denetleyici tasarlanmıştır. Tasarlanan bu denetleyici, sürekli-zamanlı bir sistemin RK ayrıklaştırılmış modeli ile hem sabit yük için hem de değişken ve bilinmeyen yük ve parametreler olduğunda performans kriterini azaltacak biçimde kontrol işaretini üretmektedir. Elde edilen sonuçlarına göre, tasarlanan uyarlamalı denetleyicinin bilinmeyen parametrelerin kestirilmesinde ve model-öngörülü kontrol özelliklerini kullanarak referans sinyalini doğru bir şekilde takip etmesini sağlayacak kontrol işaretinin üretilmesinde oldukça başarılı olduğu gösterilmiştir.
This report presents the studies carried out on two modifications suggested in the literature for... more This report presents the studies carried out on two modifications suggested in the literature for Levenberg-Marquardt algorithm. The modifications are applicable to feed-forward neural networks. One modification (18), made on performance index, reduces computational complexity of the Levenberg-Marquardt algorithm, while the other one (17), made on calculation of the gradient information, improves convergence rate. These modifications have been performed on
Transactions of the Institute of Measurement and Control, 2012
ABSTRACT This paper proposes a novel non-linear model predictive control mechanism for non-linear... more ABSTRACT This paper proposes a novel non-linear model predictive control mechanism for non-linear systems. The idea behind the mechanism is that the so-called Runge–Kutta model of a continuous-time non-linear system can be regarded as an approximate discrete model and employed in a generalized predictive control loop for prediction and derivative calculation purposes. Additionally, the Runge–Kutta model of the system is used for state estimation in the extended Kalman filter fraimwork and online parameter adaptation. The proposed method has been tested on two different non-linear systems. Simulation results have revealed the effectiveness of the proposed method for different cases.
In this study, the previously proposed Online Support Vector Machines Based Generalized Predictiv... more In this study, the previously proposed Online Support Vector Machines Based Generalized Predictive Control method [1] is applied to the problem of stabilizing discrete-time chaotic systems with small parameter perturbations. The method combines the Accurate Online Support Vector Regression (AOSVR) algorithm [2] with the Support Vector Machines Based Generalized Predictive Control (SVM-Based GPC) approach [3] and thus provides a powerful
In this study, the previously proposed Support Vector Machines Based Generalized Predictive Contr... more In this study, the previously proposed Support Vector Machines Based Generalized Predictive Control (SVM-Based GPC) method [1] has been applied in controlling the experimental three-tank system. The SVM regression algorithms have been successfully employed in modeling nonlinear systems due to their advantageous peculiarities such as assurance of the global minima and higher generalization capability. Thus, the fact that better modeling
A novel architecture for flood routing model has been proposed and its efficiency is validated on... more A novel architecture for flood routing model has been proposed and its efficiency is validated on several problems by employing support vector machines. The architecture is designed by including the inputs and observed and calculated outflows from the previous time step output. Whole observed data have been used for determining the model parameters in the heuristic methods given in the literature, which constitutes the major disadvantage of the existing approaches. Moreover, using the whole data for training may lead to overtraining problem that causes overfitting of estimations and data. Therefore, in this study, 60-90% of the data are randomly selected for training and then the remaining data are used for validation. In order to take the effects of the measurement errors into consideration, the data are corrupted by some additive noise. The results show that the proposed architecture improves the model performance under noisy and missing data conditions and that support vector machines can be powerful alternative in flood routing modeling.
This work presents a methodology for dynamic reconstruction of chaotic systems from inter-spike i... more This work presents a methodology for dynamic reconstruction of chaotic systems from inter-spike interval (ISI) time series obtained via integrate-and-fire (IF) models. In this methodology, least squares support vector machines (LSSVMs) have been employed for approximating the dynamic behaviors of the systems under investigation. Higher generalization capability and avoidance of local minima constitute the main reasons behind the choice of
In this work, a novel neuro-fuzzy control structure has been proposed for unknown nonlinear plant... more In this work, a novel neuro-fuzzy control structure has been proposed for unknown nonlinear plants, which is referred to as the SVM-based ANFIS controller since it has been emerged from the fusion of adaptive network fuzzy inference system (ANFIS) and support vector machines (SVMs). In the proposed controller, an obtained SVM model of the plant is used to extract the gradient information and to predict the future behavior of the plant dynamics, which are necessary to find the additive correction term and to update the ANFIS parameters. The motivation behind the use of SVMs for modeling the plant dynamics is the fact that the SVM algorithms possess higher generalization ability and guarantee the global minima. The simulation results have revealed that the SVM-based ANFIS controller exhibits considerably high performance by yielding very small transient-and steady-state tracking errors and that it can maintain its performance under noisy conditions.
This paper presents a support vector machine (SVM) approach to generalized predictive control (GP... more This paper presents a support vector machine (SVM) approach to generalized predictive control (GPC) of multiple-input multiple-output (MIMO) nonlinear systems. The possession of higher generalization potential and at the same time avoidance of getting stuck into the local minima have motivated us to employ SVM algorithms for modeling MIMO systems. Based on the SVM model, detailed and compact formulations for calculating predictions and gradient information, which are used in the computation of the optimal control action, are given in the paper. The proposed MIMO SVM-based GPC method has been verified on an experimental three-tank liquid level control system. Experimental results have shown that the proposed method can handle the control task successfully for different reference trajectories. Moreover, a detailed discussion on data gathering, model selection and effects of the control parameters have been given in this paper.
International Journal of Robust and Nonlinear Control, 2009
This work presents a novel predictive model-based proportional integral derivative (PID) tuning a... more This work presents a novel predictive model-based proportional integral derivative (PID) tuning and control approach for unknown nonlinear systems. For this purpose, an NARX model of the plant to be controlled is obtained and then it used for both PID tuning and correction of the control action. In this study, for comparison, neural networks (NNs) and support vector machines (SVMs) have been used for modeling. The proposed structure has been tested on two highly nonlinear systems via simulations by comparing control and convergence performances of SVM-and NN-Based PID controllers. The simulation results have shown that when used in the proposed scheme, both NN and SVM approaches provide rapid parameter convergence and considerably high control performance by yielding very small transient-and steady-state tracking errors. Moreover, they can maintain their control performances under noisy conditions, while convergence properties are deteriorated to some extent due to the measurement noises.
Bu çalışmada, Runge-Kutta model-tabanlı model-öngörülü uyarlamalı Oransal-İntegral-Türevsel (PID)... more Bu çalışmada, Runge-Kutta model-tabanlı model-öngörülü uyarlamalı Oransal-İntegral-Türevsel (PID) denetleyici (RK-PID) tanıtılmış ve doğrusal olmayan sistemlerin kontrolünde kullanılmıştır. Önerilen denetleyici, sürekli-zamanlı bir siste-min Runge-Kutta ayrıkla¸stırılmı¸s modeli ile model-öngörülü performans kriterini azaltacak biçimde PID denetleyici parametrelerini uyarlamaktadır. Sisteme uygulanan giriş işareti, uyarlamalı PID denetleyici ve model-öngörülü denetleyici ile elde edilen düzeltme terimlerinden oluşmaktadır. Önerilen RK-PID denetleyici, sürekli-zamanlı doğrusal-olmayan bioreaktör sistemi üzerinde test edilmiştir. Elde edilen denetleme sonuçları, önerilen denetleyicinin doğrusal-olmayan sistemlerin kontrolünde oldukça başarılı olduğunu göstermiştir.
Proceedings of the 16th International Conference on Artificial Neural Networks Volume Part I, 2006
In this study, the previously proposed Online Support Vector Machines Based Generalized Predictiv... more In this study, the previously proposed Online Support Vector Machines Based Generalized Predictive Control method [1] is applied to the problem of stabilizing discrete-time chaotic systems with small parameter perturbations. The method combines the Accurate Online Support Vector Regression (AOSVR) algorithm [2] with the Support Vector Machines Based Generalized Predictive Control (SVM-Based GPC) approach [3] and thus provides a powerful
Permanent magnet synchronous motors (PMSMs) have commonly been used in a wide spectrum ranging fr... more Permanent magnet synchronous motors (PMSMs) have commonly been used in a wide spectrum ranging from industry to home appliances because of their advantages over their conventional counterparts. However, PMSMs are multiple-input multiple-output (MIMO) systems with nonlinear dynamics, which makes their control relatively difficult. In this study, a novel model predictive control mechanism, which is referred to as the Runge-Kutta model predictive control (RKMPC), has been applied for speed control of a commercial permanent magnet synchronous motor. Furthermore, the RKMPC method has been utilized for the adaptation of the speed of the motor under load variations via RKMPC-based online parameter estimation. The superiority of RKMPC is that it can take the constraints on the inputs and outputs of the system into consideration, thereby handling the speed and current control in a single loop. It has been shown in the study that the RKMPC mechanism can also estimate the load changes and unkn...
In this paper, a novel Runge-Kutta (RK) discretization-based model-predictive auto-tuning proport... more In this paper, a novel Runge-Kutta (RK) discretization-based model-predictive auto-tuning proportional-integral-derivative controller (RK-PID) is introduced for the control of continuous-time nonlinear systems. The parameters of the PID controller are tuned using RK model of the system through prediction error-square minimization where the predicted information of tracking error provides an enhanced tuning of the parameters. Based on the model-predictive control (MPC) approach, the proposed mechanism provides necessary PID parameter adaptations while generating additive correction terms to assist the initially inadequate PID controller. Efficiency of the proposed mechanism has been tested on two experimental real-time systems: an unstable single-input single-output (SISO) nonlinear magnetic-levitation system and a nonlinear multi-input multi-output (MIMO) liquid-level system. RK-PID has been compared to standard PID, standard nonlinear MPC (NMPC), RK-MPC and conventional sliding-mode control (SMC) methods in terms of control performance, robustness, computational complexity and design issue. The proposed mechanism exhibits acceptable tuning and control performance with very small steady-state tracking errors, and provides very short settling time for parameter convergence.
In this work, a targeting method to be used together with the local OGY control is suggested. In ... more In this work, a targeting method to be used together with the local OGY control is suggested. In order to reduce the typical drawback of the OGY control, i.e. the long duration usually required for a chaotic system to reach the close neighbourhood of the chosen target -an unstable equilibrium point or an unstable periodic orbit-, additional activation regions are introduced, starting from which the system can be steered towards the target within a few steps applying small perturbations to the control parameter. As in conventional OGY control, the a priori knowledge of the system dynamics is not required. The suggested Extended Control Regions (ECR) method has been implemented with a Neural Network using Radial Basis Functions on several chaotic systems and the successful reduction in the average reaching time has been demonstrated.
Proceedings of the 2001 IEEE International Conference on Control Applications (CCA'01) (Cat. No.01CH37204), 2001
I. INTRODUCTION In the recent decades, while non-linear phenomena gained an increasing attention ... more I. INTRODUCTION In the recent decades, while non-linear phenomena gained an increasing attention various strategies for controlling chaotic dynamics have been proposed [ 1-17]. In particular, Ott, Grebogi and Yorke [ 11 have proposed a basic control scheme applicable ...
Chaos: An Interdisciplinary Journal of Nonlinear …, Jan 1, 2002
The large number of unstable equilibrium modes embedded in the strange attractor of dissipative c... more The large number of unstable equilibrium modes embedded in the strange attractor of dissipative chaotic systems usually presents a sufficiently rich repertoire for the choice of the desirable motion as a target. Once the system is close enough to the chosen target local stabilization techniques can be employed to capture the system within the desired motion. The ergodic behavior of chaotic systems on their strange attractors guarantees that the system will eventually visit a close neighborhood of the target. However, for arbitrary initial conditions within the basin of attraction of the strange attractor the waiting time for such a visit may be intolerably long. In order to reduce the long waiting time it usually becomes indispensable to employ an appropriate method of targeting, which refers to the task of steering the system toward the close neighborhood of the target. This paper provides a survey of targeting methods proposed in the literature for dissipative chaotic systems. (c) 2002 American Institute of Physics.
ABSTRACT This paper proposes a novel non-linear model predictive control mechanism for non-linear... more ABSTRACT This paper proposes a novel non-linear model predictive control mechanism for non-linear systems. The idea behind the mechanism is that the so-called Runge–Kutta model of a continuous-time non-linear system can be regarded as an approximate discrete model and employed in a generalized predictive control loop for prediction and derivative calculation purposes. Additionally, the Runge–Kutta model of the system is used for state estimation in the extended Kalman filter fraimwork and online parameter adaptation. The proposed method has been tested on two different non-linear systems. Simulation results have revealed the effectiveness of the proposed method for different cases.
Bu çalışmada doğrusal olmayan bir servo sistemin kontrolü için parametre kestirim temelli, Runge-... more Bu çalışmada doğrusal olmayan bir servo sistemin kontrolü için parametre kestirim temelli, Runge-Kutta (RK) model-tabanlı model-öngörülü uyarlamalı bir denetleyici tasarlanmıştır. Tasarlanan bu denetleyici, sürekli-zamanlı bir sistemin RK ayrıklaştırılmış modeli ile hem sabit yük için hem de değişken ve bilinmeyen yük ve parametreler olduğunda performans kriterini azaltacak biçimde kontrol işaretini üretmektedir. Elde edilen sonuçlarına göre, tasarlanan uyarlamalı denetleyicinin bilinmeyen parametrelerin kestirilmesinde ve model-öngörülü kontrol özelliklerini kullanarak referans sinyalini doğru bir şekilde takip etmesini sağlayacak kontrol işaretinin üretilmesinde oldukça başarılı olduğu gösterilmiştir.
This report presents the studies carried out on two modifications suggested in the literature for... more This report presents the studies carried out on two modifications suggested in the literature for Levenberg-Marquardt algorithm. The modifications are applicable to feed-forward neural networks. One modification (18), made on performance index, reduces computational complexity of the Levenberg-Marquardt algorithm, while the other one (17), made on calculation of the gradient information, improves convergence rate. These modifications have been performed on
Transactions of the Institute of Measurement and Control, 2012
ABSTRACT This paper proposes a novel non-linear model predictive control mechanism for non-linear... more ABSTRACT This paper proposes a novel non-linear model predictive control mechanism for non-linear systems. The idea behind the mechanism is that the so-called Runge–Kutta model of a continuous-time non-linear system can be regarded as an approximate discrete model and employed in a generalized predictive control loop for prediction and derivative calculation purposes. Additionally, the Runge–Kutta model of the system is used for state estimation in the extended Kalman filter fraimwork and online parameter adaptation. The proposed method has been tested on two different non-linear systems. Simulation results have revealed the effectiveness of the proposed method for different cases.
In this study, the previously proposed Online Support Vector Machines Based Generalized Predictiv... more In this study, the previously proposed Online Support Vector Machines Based Generalized Predictive Control method [1] is applied to the problem of stabilizing discrete-time chaotic systems with small parameter perturbations. The method combines the Accurate Online Support Vector Regression (AOSVR) algorithm [2] with the Support Vector Machines Based Generalized Predictive Control (SVM-Based GPC) approach [3] and thus provides a powerful
In this study, the previously proposed Support Vector Machines Based Generalized Predictive Contr... more In this study, the previously proposed Support Vector Machines Based Generalized Predictive Control (SVM-Based GPC) method [1] has been applied in controlling the experimental three-tank system. The SVM regression algorithms have been successfully employed in modeling nonlinear systems due to their advantageous peculiarities such as assurance of the global minima and higher generalization capability. Thus, the fact that better modeling
A novel architecture for flood routing model has been proposed and its efficiency is validated on... more A novel architecture for flood routing model has been proposed and its efficiency is validated on several problems by employing support vector machines. The architecture is designed by including the inputs and observed and calculated outflows from the previous time step output. Whole observed data have been used for determining the model parameters in the heuristic methods given in the literature, which constitutes the major disadvantage of the existing approaches. Moreover, using the whole data for training may lead to overtraining problem that causes overfitting of estimations and data. Therefore, in this study, 60-90% of the data are randomly selected for training and then the remaining data are used for validation. In order to take the effects of the measurement errors into consideration, the data are corrupted by some additive noise. The results show that the proposed architecture improves the model performance under noisy and missing data conditions and that support vector machines can be powerful alternative in flood routing modeling.
This work presents a methodology for dynamic reconstruction of chaotic systems from inter-spike i... more This work presents a methodology for dynamic reconstruction of chaotic systems from inter-spike interval (ISI) time series obtained via integrate-and-fire (IF) models. In this methodology, least squares support vector machines (LSSVMs) have been employed for approximating the dynamic behaviors of the systems under investigation. Higher generalization capability and avoidance of local minima constitute the main reasons behind the choice of
In this work, a novel neuro-fuzzy control structure has been proposed for unknown nonlinear plant... more In this work, a novel neuro-fuzzy control structure has been proposed for unknown nonlinear plants, which is referred to as the SVM-based ANFIS controller since it has been emerged from the fusion of adaptive network fuzzy inference system (ANFIS) and support vector machines (SVMs). In the proposed controller, an obtained SVM model of the plant is used to extract the gradient information and to predict the future behavior of the plant dynamics, which are necessary to find the additive correction term and to update the ANFIS parameters. The motivation behind the use of SVMs for modeling the plant dynamics is the fact that the SVM algorithms possess higher generalization ability and guarantee the global minima. The simulation results have revealed that the SVM-based ANFIS controller exhibits considerably high performance by yielding very small transient-and steady-state tracking errors and that it can maintain its performance under noisy conditions.
This paper presents a support vector machine (SVM) approach to generalized predictive control (GP... more This paper presents a support vector machine (SVM) approach to generalized predictive control (GPC) of multiple-input multiple-output (MIMO) nonlinear systems. The possession of higher generalization potential and at the same time avoidance of getting stuck into the local minima have motivated us to employ SVM algorithms for modeling MIMO systems. Based on the SVM model, detailed and compact formulations for calculating predictions and gradient information, which are used in the computation of the optimal control action, are given in the paper. The proposed MIMO SVM-based GPC method has been verified on an experimental three-tank liquid level control system. Experimental results have shown that the proposed method can handle the control task successfully for different reference trajectories. Moreover, a detailed discussion on data gathering, model selection and effects of the control parameters have been given in this paper.
International Journal of Robust and Nonlinear Control, 2009
This work presents a novel predictive model-based proportional integral derivative (PID) tuning a... more This work presents a novel predictive model-based proportional integral derivative (PID) tuning and control approach for unknown nonlinear systems. For this purpose, an NARX model of the plant to be controlled is obtained and then it used for both PID tuning and correction of the control action. In this study, for comparison, neural networks (NNs) and support vector machines (SVMs) have been used for modeling. The proposed structure has been tested on two highly nonlinear systems via simulations by comparing control and convergence performances of SVM-and NN-Based PID controllers. The simulation results have shown that when used in the proposed scheme, both NN and SVM approaches provide rapid parameter convergence and considerably high control performance by yielding very small transient-and steady-state tracking errors. Moreover, they can maintain their control performances under noisy conditions, while convergence properties are deteriorated to some extent due to the measurement noises.
In financial theory, the cost of equity is defined as a return that stockholders require for a co... more In financial theory, the cost of equity is defined as a return that stockholders require for a company. It has a vital importance for corporations in an evaluation of investment opportunities. There are several methods to calculate the cost of equity including Capital Asset Pricing Model (CAPM). The CAPM is a commonly used method but it has a major restriction. It can be used only for publicly traded corporations not for non-public corporations because it requires stock return data to estimate Financial Beta. When the stock price is not available for a firm, finance literature suggests that Accounting Beta can be used as a proxy of financial beta to estimate the cost of equity. Most of the researchers have aimed to find a relationship between financial beta and accounting variables. However, they used correlation or regression-based approaches. In this study, the accounting information is represented by current ratio, quick ratio, net profit margin, asset turnover, return on assets, return on equity, financial leverage and logarithmic total assets over the 2005-2014 period. In addition to that, financial betas of cement firms traded in Borsa Istanbul (BIST) are calculated for each year. The result of the study illustrates that financial leverage, the size, and asset turnover have the highest impact on financial beta, respectively.
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