Zakwan Skaf - Academia.edu (original) (raw)
Papers by Zakwan Skaf
International Conference on Aerospace Sciences & Aviation Technology, May 1, 2011
International journal of prognostics and health management, Nov 16, 2020
Fault diagnosis typically consists of fault detection, isolation and identification. Fault detect... more Fault diagnosis typically consists of fault detection, isolation and identification. Fault detection and isolation determine the presence of a fault in a system and the location of the fault. Fault identification then aims at determining the severity level of the fault. In a practical sense, a fault is a conditional interruption of the system ability to achieve a required function under specified operating condition; degradation is the deviation of one or more characteristic parameters of the component from acceptable conditions and is often a main cause for fault generation. A fault occurs when the degradation exceeds an allowable threshold. From the point a new aircraft takes off for the first time all of its components start to degrade, and yet in almost all studies it is presumed that we can identify a single fault in isolation, i.e. without considering multi-component degradation in the system. This paper proposes a probabilistic framework to identify a single fault in an aircraft fuel system with consideration of multi-component degradation. Based on the conditional probabilities of sensor readings for a specific fault, a Bayesian method is presented to integrate distributed sensory information and calculate the likelihood of all possible fault severity levels. The proposed framework is implemented on an experimental aircraft fuel rig which illustrates the applicability of the proposed method. _____________________ Yufei Lin et al. This is an open-access article distributed under the terms of the Creative Commons Attribution 3.0 United States License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Procedia Manufacturing, 2018
Under the concept of "Industry 4.0", production processes will be pushed to be increasingly inter... more Under the concept of "Industry 4.0", production processes will be pushed to be increasingly interconnected, information based on a real time basis and, necessarily, much more efficient. In this context, capacity optimization goes beyond the traditional aim of capacity maximization, contributing also for organization's profitability and value. Indeed, lean management and continuous improvement approaches suggest capacity optimization instead of maximization. The study of capacity optimization and costing models is an important research topic that deserves contributions from both the practical and theoretical perspectives. This paper presents and discusses a mathematical model for capacity management based on different costing models (ABC and TDABC). A generic model has been developed and it was used to analyze idle capacity and to design strategies towards the maximization of organization's value. The trade-off capacity maximization vs operational efficiency is highlighted and it is shown that capacity optimization might hide operational inefficiency.
UKACC International Conference on CONTROL 2010, 2010
In this paper, a new fault tolerant controller (FTC) algorithm for general stochastic nonlinear s... more In this paper, a new fault tolerant controller (FTC) algorithm for general stochastic nonlinear systems is studied. Different from the existing FTC methods, the measured information is the probability density functions (PDFs) of the system output rather than its value, where the radial basis functions (RBFs) neural network technique is proposed so that the output PDFs can be formulated in terms of the dynamic weighings, so that the problem is transformed into a nonlinear FTC problem subject to the weight dynamical systems. The main objective of FTC requires detecting the occurrence of faults and maintaining the performance of the system in the presence of faults at a satisfying level. The FTC design consists of two steps. The first step is fault detection and diagnosis (FDD), which can produce an alarm when there is a fault in the system and also locate which component has a fault. The second step is to adapt the controller to the faulty case so that the system is able to achieve its target. A linear matrix inequality (LMI) based feasible FTC method is applied such that the fault can be detected and diagnosed. An illustrated example is included to demonstrate the use of control algorithm, and satisfactory results have been obtained.
2022 Advances in Science and Engineering Technology International Conferences (ASET), 2022
Solar energy is renewable, clean, and friendly to the environment. Utilizing solar energy is a ma... more Solar energy is renewable, clean, and friendly to the environment. Utilizing solar energy is a major step toward reducing global warming because it reduces pollution. The smart city concept presents a novel idea for renewable energy, such as Photovoltaic (PV) technologies. The smart campus is one of the areas of focus in smart cities. In this context, the smart campus is a term used to refer to the teaching environment and application service systems, where dynamic interaction between people and the surrounding service develops intelligent teaching, learning, and campus life environment. However, some researchers refer to the smart campus to replace the current energy sources with more sustainable and environmentally friendly solutions. This paper presents an overview of a smart green campus's concept by integrating the concepts of green energy generation and smart system application. This would enhance the building efficiency, utilize more renewable energy technology and advanced digital solution, minimize the environmental impact and operation cost. This paper uses the Higher Colleges of Technology (HCT) campus in Sharjah Men campus (SMC) as a use case study to demonstrate the vision of the smart green campus. The key areas of the campus considered in the study are campus building, streets and outdoor areas, and campus services. The proposed concept of a smart green campus will focus on the IoT-enabled sensor devices proposed to each potential application in the campus. The proposed vision of the smart green campus serves the community better by providing different innovative systems for the people and facilitating the country's development. Furthermore, the vision caters to the core infrastructure of the campus, such as the buildings, the roads, and the Mosque, while providing its members with a decent quality of life, a clean and sustainable environment, and innovative systems. The case study shows a 63.7% saving in electricity when using solar energy to generate electricity and implementing the innovative applications to the smart green campus. Also, it shows a reduction in the emission and carbon dioxide CO2 released into the air as a direct result of electricity generation to 0.02.
IFAC-PapersOnLine, 2020
Abstract Aircraft fault detection and prediction is a critical element of preventing failures, re... more Abstract Aircraft fault detection and prediction is a critical element of preventing failures, reducing maintenance costs, and increasing fleet availability. This paper considers a problem of rare failure prediction in the context of aircraft predictive maintenance. It presents a novel approach of predicting extremely rare failures, based on combining two deep learning techniques, auto-encoder (AE) and Bidirectional Gated Recurrent Unit (BGRU) network. AE is modified and trained to detect rare failure, and the result from AE is fed into the BGRU to predict the next occurrence of failure. The applicability of the proposed approach is evaluated using real-world test cases of log-based warning and failure messages obtained from the aircraft central maintenance system fleet database and the records of maintenance history. The proposed AE-BGRU model is compared with other similar deep learning methods, the proposed approach is 25% better in precision, 14% in the recall, and 3% in G-mean. The result also shows robustness in predicting failure within a defined useful period.
2010 8th World Congress on Intelligent Control and Automation, 2010
AbstractIn this paper, a new algorithm for an adaptive Proportional-Integrator (PI)controller fo... more AbstractIn this paper, a new algorithm for an adaptive Proportional-Integrator (PI)controller for nonlinear systems subjected to stochastic non-Gaussian disturbance is studied. The minimum entropy control is applied to decrease the closed-loop tracking error under an iterative ...
IEEE Conference on Decision and Control and European Control Conference, 2011
In this paper, a new algorithm for an adaptive PI controller for nonlinear systems subject to sto... more In this paper, a new algorithm for an adaptive PI controller for nonlinear systems subject to stochastic non-Gaussian disturbance is studied. The minimum entropy control is applied to decrease the closed-loop tracking error on an ILC basis. The key issue here is to divide the control horizon into a number of equal time intervals called batches. Within each interval, there are a fixed number of sample points. The design procedure is divided into two main algorithms, within each batch and between any two adjacent batches. A D-type ILC law is employed to tune the PI controller coefficients between two adjacent batches. However, within each batch, the PI coefficients are fixed. A sufficient condition is established to guarantee the stability of the closed-loop system. An analysis of the ILC convergence is carried out. Two-link robot manipulator example is included to demonstrate the use of the control algorithm, and satisfactory results are obtained.
Quality and Reliability Engineering International, 2012
Failure prediction (i.e. prognostics) is critical for effective maintenance because it greatly im... more Failure prediction (i.e. prognostics) is critical for effective maintenance because it greatly impacts the competitiveness of organizations through its direct connection with operating and support costs, system availability, and operational safety. In recent years, research has focused on state-based prognostics that forecast future progression by first identifying the current state. The duration spent in a state is a factor that influences the expected time to be spent in that state in the future; however, previous works on state-based prognostics have ignored the effect of duration. Hidden Markov Models are the most famous state-based prognostics methods in the literature with practicality problems such as computational complexity, requirement of excessive data, and dependency on initialization. This paper presents a new, simple and easy to implement state-based prognostic method using state duration information. The presented method is applied to two real systems (railway turnout systems and drill bits), and the results are compared with the existing methods presented in the literature. The results show that the presented method outperforms the existing methods.
This paper presents a comparative study of six different linear observers. The studied observers ... more This paper presents a comparative study of six different linear observers. The studied observers are Luenberger Observer, Kalman (Filter) Observer, Unknown Input Observer, Augmented Robust Observer, High Gain Observer and Sensitive High Gain Observer. A Matlab simulation of a DC motor model is undertaken to verify the performance of the designed observers. The Comparisons were carried out different conditions in terms of white noise as disturbance, where the Probability Density Function (PDF) of estimated residuals has been used. For additive fault only the amplitude of residuals has been considered. The simulation results are given to show and compare the effectiveness of these observers on the speed of the servo DC motor.
Expert Systems, 2007
This paper gives an integrated view of implementing automated diagnostic systems for clinical dec... more This paper gives an integrated view of implementing automated diagnostic systems for clinical decision-making. Because of the importance of making the right decision, better classification procedures are necessary for clinical decisions. The major objective of the paper is to be a guide for readers who want to develop an automated decision support system for clinical practice. The purpose was to determine an optimum classification scheme with high diagnostic accuracy for this problem. Several different classification algorithms were tested and benchmarked for their performance. The performance of the classification algorithms is illustrated on two data sets: the Pima Indians diabetes and the Wisconsin breast cancer. The present research demonstrates that the support vector machines achieved diagnostic accuracies which were higher than those of other automated diagnostic systems.
Mechanical Systems and Signal Processing, 2022
9 Declaration 10 Copyright 11 Acknowledgements 12 Publications During PhD Study 13 Notation 15 Li... more 9 Declaration 10 Copyright 11 Acknowledgements 12 Publications During PhD Study 13 Notation 15 List of Abbreviations 16 Dedication 17
2010 8th World Congress on Intelligent Control and Automation, 2010
This paper studies and compares three nonlinear observers (Nonlinear Lyapunov Observer (NLO), Lip... more This paper studies and compares three nonlinear observers (Nonlinear Lyapunov Observer (NLO), Lipschitz Observer (LIO) and Partial Lipschitz Observer (PLIO)) applied to nonlinear model of the DC servo motor. The considered criteria of computations for white noise is the amplitude of the residual and the estimated shape of residual and error probability density functions (PDF) which is estimated by Kernel
Neural Computing and Applications
The use of aircraft operation logs to develop a data-driven model to predict probable failures th... more The use of aircraft operation logs to develop a data-driven model to predict probable failures that could cause interruption poses many challenges and has yet to be fully explored. Given that aircraft is high-integrity assets, failures are exceedingly rare. Hence, the distribution of relevant log data containing prior signs will be heavily skewed towards the typical (healthy) scenario. Thus, this study presents a novel deep learning technique based on the auto-encoder and bidirectional gated recurrent unit networks to handle extremely rare failure predictions in aircraft predictive maintenance modelling. The auto-encoder is modified and trained to detect rare failures, and the result from the auto-encoder is fed into the convolutional bidirectional gated recurrent unit network to predict the next occurrence of failure. The proposed network architecture with the rescaled focal loss addresses the imbalance problem during model training. The effectiveness of the proposed method is eval...
Deep learning approaches are continuously achieving state-of-the-art performance in aerospace pre... more Deep learning approaches are continuously achieving state-of-the-art performance in aerospace predictive maintenance modelling. However, the data imbalance distribution issue is still a challenge. It causes performance degradation in predictive models, resulting in unreliable prognostics which prevents predictive models from being widely deployed in realtime aircraft systems. The imbalanced classification problem arises when the distribution of the classes present in the datasets is not uniform, such that the total number of instances in a class is significantly lower than those belonging to the other classes. It becomes more challenging when the imbalance ratio is extreme. This paper proposes a deep learning approach using rescaled Long Short Term Memory (LSTM) modelling for predicting aircraft component replacement under imbalanced dataset constraint. The new approach modifies prediction of each class using rescale weighted cross-entropy loss, which controls the weight of majority...
— A new design of a fault tolerant control (FTC)-based an adaptive, fixed-structure PI controller... more — A new design of a fault tolerant control (FTC)-based an adaptive, fixed-structure PI controller, with constraints on the state vector for nonlinear discrete-time system subject to stochastic non-Gaussian disturbance is studied. The objective of the reliable control algorithm scheme is to design a control signal such that the actual probability density function (PDF) of the system is made as close as possible to a desired PDF, and make the tracking performance converge to zero, not only when all components are functional but also in case of admissible faults. A Linear Matrix Inequality (LMI)-based FTC method is presented to ensure that the fault can be estimated and compensated for. A radial basis function (RBF) neural network is used to approximate the output PDF of the system. Thus, the aim of the output PDF control will be a RBF weight control with an adaptive tuning of the basis function parameters. The key issue here is to divide the control horizon into a number of equal time...
International Conference on Aerospace Sciences & Aviation Technology, May 1, 2011
International journal of prognostics and health management, Nov 16, 2020
Fault diagnosis typically consists of fault detection, isolation and identification. Fault detect... more Fault diagnosis typically consists of fault detection, isolation and identification. Fault detection and isolation determine the presence of a fault in a system and the location of the fault. Fault identification then aims at determining the severity level of the fault. In a practical sense, a fault is a conditional interruption of the system ability to achieve a required function under specified operating condition; degradation is the deviation of one or more characteristic parameters of the component from acceptable conditions and is often a main cause for fault generation. A fault occurs when the degradation exceeds an allowable threshold. From the point a new aircraft takes off for the first time all of its components start to degrade, and yet in almost all studies it is presumed that we can identify a single fault in isolation, i.e. without considering multi-component degradation in the system. This paper proposes a probabilistic framework to identify a single fault in an aircraft fuel system with consideration of multi-component degradation. Based on the conditional probabilities of sensor readings for a specific fault, a Bayesian method is presented to integrate distributed sensory information and calculate the likelihood of all possible fault severity levels. The proposed framework is implemented on an experimental aircraft fuel rig which illustrates the applicability of the proposed method. _____________________ Yufei Lin et al. This is an open-access article distributed under the terms of the Creative Commons Attribution 3.0 United States License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Procedia Manufacturing, 2018
Under the concept of "Industry 4.0", production processes will be pushed to be increasingly inter... more Under the concept of "Industry 4.0", production processes will be pushed to be increasingly interconnected, information based on a real time basis and, necessarily, much more efficient. In this context, capacity optimization goes beyond the traditional aim of capacity maximization, contributing also for organization's profitability and value. Indeed, lean management and continuous improvement approaches suggest capacity optimization instead of maximization. The study of capacity optimization and costing models is an important research topic that deserves contributions from both the practical and theoretical perspectives. This paper presents and discusses a mathematical model for capacity management based on different costing models (ABC and TDABC). A generic model has been developed and it was used to analyze idle capacity and to design strategies towards the maximization of organization's value. The trade-off capacity maximization vs operational efficiency is highlighted and it is shown that capacity optimization might hide operational inefficiency.
UKACC International Conference on CONTROL 2010, 2010
In this paper, a new fault tolerant controller (FTC) algorithm for general stochastic nonlinear s... more In this paper, a new fault tolerant controller (FTC) algorithm for general stochastic nonlinear systems is studied. Different from the existing FTC methods, the measured information is the probability density functions (PDFs) of the system output rather than its value, where the radial basis functions (RBFs) neural network technique is proposed so that the output PDFs can be formulated in terms of the dynamic weighings, so that the problem is transformed into a nonlinear FTC problem subject to the weight dynamical systems. The main objective of FTC requires detecting the occurrence of faults and maintaining the performance of the system in the presence of faults at a satisfying level. The FTC design consists of two steps. The first step is fault detection and diagnosis (FDD), which can produce an alarm when there is a fault in the system and also locate which component has a fault. The second step is to adapt the controller to the faulty case so that the system is able to achieve its target. A linear matrix inequality (LMI) based feasible FTC method is applied such that the fault can be detected and diagnosed. An illustrated example is included to demonstrate the use of control algorithm, and satisfactory results have been obtained.
2022 Advances in Science and Engineering Technology International Conferences (ASET), 2022
Solar energy is renewable, clean, and friendly to the environment. Utilizing solar energy is a ma... more Solar energy is renewable, clean, and friendly to the environment. Utilizing solar energy is a major step toward reducing global warming because it reduces pollution. The smart city concept presents a novel idea for renewable energy, such as Photovoltaic (PV) technologies. The smart campus is one of the areas of focus in smart cities. In this context, the smart campus is a term used to refer to the teaching environment and application service systems, where dynamic interaction between people and the surrounding service develops intelligent teaching, learning, and campus life environment. However, some researchers refer to the smart campus to replace the current energy sources with more sustainable and environmentally friendly solutions. This paper presents an overview of a smart green campus's concept by integrating the concepts of green energy generation and smart system application. This would enhance the building efficiency, utilize more renewable energy technology and advanced digital solution, minimize the environmental impact and operation cost. This paper uses the Higher Colleges of Technology (HCT) campus in Sharjah Men campus (SMC) as a use case study to demonstrate the vision of the smart green campus. The key areas of the campus considered in the study are campus building, streets and outdoor areas, and campus services. The proposed concept of a smart green campus will focus on the IoT-enabled sensor devices proposed to each potential application in the campus. The proposed vision of the smart green campus serves the community better by providing different innovative systems for the people and facilitating the country's development. Furthermore, the vision caters to the core infrastructure of the campus, such as the buildings, the roads, and the Mosque, while providing its members with a decent quality of life, a clean and sustainable environment, and innovative systems. The case study shows a 63.7% saving in electricity when using solar energy to generate electricity and implementing the innovative applications to the smart green campus. Also, it shows a reduction in the emission and carbon dioxide CO2 released into the air as a direct result of electricity generation to 0.02.
IFAC-PapersOnLine, 2020
Abstract Aircraft fault detection and prediction is a critical element of preventing failures, re... more Abstract Aircraft fault detection and prediction is a critical element of preventing failures, reducing maintenance costs, and increasing fleet availability. This paper considers a problem of rare failure prediction in the context of aircraft predictive maintenance. It presents a novel approach of predicting extremely rare failures, based on combining two deep learning techniques, auto-encoder (AE) and Bidirectional Gated Recurrent Unit (BGRU) network. AE is modified and trained to detect rare failure, and the result from AE is fed into the BGRU to predict the next occurrence of failure. The applicability of the proposed approach is evaluated using real-world test cases of log-based warning and failure messages obtained from the aircraft central maintenance system fleet database and the records of maintenance history. The proposed AE-BGRU model is compared with other similar deep learning methods, the proposed approach is 25% better in precision, 14% in the recall, and 3% in G-mean. The result also shows robustness in predicting failure within a defined useful period.
2010 8th World Congress on Intelligent Control and Automation, 2010
AbstractIn this paper, a new algorithm for an adaptive Proportional-Integrator (PI)controller fo... more AbstractIn this paper, a new algorithm for an adaptive Proportional-Integrator (PI)controller for nonlinear systems subjected to stochastic non-Gaussian disturbance is studied. The minimum entropy control is applied to decrease the closed-loop tracking error under an iterative ...
IEEE Conference on Decision and Control and European Control Conference, 2011
In this paper, a new algorithm for an adaptive PI controller for nonlinear systems subject to sto... more In this paper, a new algorithm for an adaptive PI controller for nonlinear systems subject to stochastic non-Gaussian disturbance is studied. The minimum entropy control is applied to decrease the closed-loop tracking error on an ILC basis. The key issue here is to divide the control horizon into a number of equal time intervals called batches. Within each interval, there are a fixed number of sample points. The design procedure is divided into two main algorithms, within each batch and between any two adjacent batches. A D-type ILC law is employed to tune the PI controller coefficients between two adjacent batches. However, within each batch, the PI coefficients are fixed. A sufficient condition is established to guarantee the stability of the closed-loop system. An analysis of the ILC convergence is carried out. Two-link robot manipulator example is included to demonstrate the use of the control algorithm, and satisfactory results are obtained.
Quality and Reliability Engineering International, 2012
Failure prediction (i.e. prognostics) is critical for effective maintenance because it greatly im... more Failure prediction (i.e. prognostics) is critical for effective maintenance because it greatly impacts the competitiveness of organizations through its direct connection with operating and support costs, system availability, and operational safety. In recent years, research has focused on state-based prognostics that forecast future progression by first identifying the current state. The duration spent in a state is a factor that influences the expected time to be spent in that state in the future; however, previous works on state-based prognostics have ignored the effect of duration. Hidden Markov Models are the most famous state-based prognostics methods in the literature with practicality problems such as computational complexity, requirement of excessive data, and dependency on initialization. This paper presents a new, simple and easy to implement state-based prognostic method using state duration information. The presented method is applied to two real systems (railway turnout systems and drill bits), and the results are compared with the existing methods presented in the literature. The results show that the presented method outperforms the existing methods.
This paper presents a comparative study of six different linear observers. The studied observers ... more This paper presents a comparative study of six different linear observers. The studied observers are Luenberger Observer, Kalman (Filter) Observer, Unknown Input Observer, Augmented Robust Observer, High Gain Observer and Sensitive High Gain Observer. A Matlab simulation of a DC motor model is undertaken to verify the performance of the designed observers. The Comparisons were carried out different conditions in terms of white noise as disturbance, where the Probability Density Function (PDF) of estimated residuals has been used. For additive fault only the amplitude of residuals has been considered. The simulation results are given to show and compare the effectiveness of these observers on the speed of the servo DC motor.
Expert Systems, 2007
This paper gives an integrated view of implementing automated diagnostic systems for clinical dec... more This paper gives an integrated view of implementing automated diagnostic systems for clinical decision-making. Because of the importance of making the right decision, better classification procedures are necessary for clinical decisions. The major objective of the paper is to be a guide for readers who want to develop an automated decision support system for clinical practice. The purpose was to determine an optimum classification scheme with high diagnostic accuracy for this problem. Several different classification algorithms were tested and benchmarked for their performance. The performance of the classification algorithms is illustrated on two data sets: the Pima Indians diabetes and the Wisconsin breast cancer. The present research demonstrates that the support vector machines achieved diagnostic accuracies which were higher than those of other automated diagnostic systems.
Mechanical Systems and Signal Processing, 2022
9 Declaration 10 Copyright 11 Acknowledgements 12 Publications During PhD Study 13 Notation 15 Li... more 9 Declaration 10 Copyright 11 Acknowledgements 12 Publications During PhD Study 13 Notation 15 List of Abbreviations 16 Dedication 17
2010 8th World Congress on Intelligent Control and Automation, 2010
This paper studies and compares three nonlinear observers (Nonlinear Lyapunov Observer (NLO), Lip... more This paper studies and compares three nonlinear observers (Nonlinear Lyapunov Observer (NLO), Lipschitz Observer (LIO) and Partial Lipschitz Observer (PLIO)) applied to nonlinear model of the DC servo motor. The considered criteria of computations for white noise is the amplitude of the residual and the estimated shape of residual and error probability density functions (PDF) which is estimated by Kernel
Neural Computing and Applications
The use of aircraft operation logs to develop a data-driven model to predict probable failures th... more The use of aircraft operation logs to develop a data-driven model to predict probable failures that could cause interruption poses many challenges and has yet to be fully explored. Given that aircraft is high-integrity assets, failures are exceedingly rare. Hence, the distribution of relevant log data containing prior signs will be heavily skewed towards the typical (healthy) scenario. Thus, this study presents a novel deep learning technique based on the auto-encoder and bidirectional gated recurrent unit networks to handle extremely rare failure predictions in aircraft predictive maintenance modelling. The auto-encoder is modified and trained to detect rare failures, and the result from the auto-encoder is fed into the convolutional bidirectional gated recurrent unit network to predict the next occurrence of failure. The proposed network architecture with the rescaled focal loss addresses the imbalance problem during model training. The effectiveness of the proposed method is eval...
Deep learning approaches are continuously achieving state-of-the-art performance in aerospace pre... more Deep learning approaches are continuously achieving state-of-the-art performance in aerospace predictive maintenance modelling. However, the data imbalance distribution issue is still a challenge. It causes performance degradation in predictive models, resulting in unreliable prognostics which prevents predictive models from being widely deployed in realtime aircraft systems. The imbalanced classification problem arises when the distribution of the classes present in the datasets is not uniform, such that the total number of instances in a class is significantly lower than those belonging to the other classes. It becomes more challenging when the imbalance ratio is extreme. This paper proposes a deep learning approach using rescaled Long Short Term Memory (LSTM) modelling for predicting aircraft component replacement under imbalanced dataset constraint. The new approach modifies prediction of each class using rescale weighted cross-entropy loss, which controls the weight of majority...
— A new design of a fault tolerant control (FTC)-based an adaptive, fixed-structure PI controller... more — A new design of a fault tolerant control (FTC)-based an adaptive, fixed-structure PI controller, with constraints on the state vector for nonlinear discrete-time system subject to stochastic non-Gaussian disturbance is studied. The objective of the reliable control algorithm scheme is to design a control signal such that the actual probability density function (PDF) of the system is made as close as possible to a desired PDF, and make the tracking performance converge to zero, not only when all components are functional but also in case of admissible faults. A Linear Matrix Inequality (LMI)-based FTC method is presented to ensure that the fault can be estimated and compensated for. A radial basis function (RBF) neural network is used to approximate the output PDF of the system. Thus, the aim of the output PDF control will be a RBF weight control with an adaptive tuning of the basis function parameters. The key issue here is to divide the control horizon into a number of equal time...