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Xiao, Bo. "Stability and performance analysis of polynomial fuzzy-model-based control systems and interval type-2 fuzzy logic systems." Thesis, King's College London (University of London), 2018. https://kclpure.kcl.ac.uk/portal/en/theses/stability-and-performance-analysis-of-polynomial-fuzzymodelbased-control-systems-and-interval-type2-fuzzy-logic-systems(1a455ca8-f27d-49aa-ab4a-8ae697aeba17).html.
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The main research objective in this thesis is to investigate the stability and performance of the interval type-2 (IT2) polynomial-fuzzy-model-based (PFMB) control system. PFMB control scheme has been developed recently around 2009 and demonstrates more potential than the traditional Takagi-Sugeno fuzzy-model-based (T-S FMB) control approach to represent the nonlinearities in the plant. Meanwhile, the IT2 fuzzy logic has also been proposed to incorporate uncertainties of the nonlinear systems into the membership functions directly. Through the IT2 PFMB control design approach, both the nonlinearity and the uncertainty in the system can be handled well. The control performance and the relaxation of stability conditions of IT2 PFMB control systems are studied and investigated in the thesis. The main contribution of the thesis is summarized in three tasks and presented as following: In the first task in Chapter 3, the stability conditions of the PFMB systems equipped with mismatched IT2 membership functions are investigated. Unlike the membership-function-independent (MFI) methods, the information and properties of IT2 membership functions are considered in the stability analysis and contained in the stability conditions in terms of sum-of-squares (SOS) based on the Lyapunov stability theory. Three methods, demonstrating their own merits, are proposed to conduct the stability analysis for the IT2 PFMB control systems and all of the methods can achieve feasible control results. All the three approaches are well explained, which offers the reader systematic ways to include the information of the membership functions into the analysis. In addition, all the approaches are compared and the pros and cons are presented to help the reader choose the most appropriate approach in the applications. In the second task presented in Chapter 4, the membership-functions-dependent (MFD) methods have been proceeded to the tracking control problems and the output feedback tracking issues of IT2 PFMB fuzzy control systems are investigated. The output-feedback IT2 polynomial fuzzy controller connected with the nonlinear plant in a closed loop drives the system states of the nonlinear plant to track those of the stable reference model. The system stability is investigated based on the Lyapunov stability theory under the SOS-based analysis approach and the SOSbased stability conditions are derived subject to a prescribed H1 performance. Like in the first work, the information of membership functions is also included in the analysis to facilitate the analysis and help improve the tracking performance in terms of H1 performance. Considering the implementation of the mentioned control schemes on digital computers, the sampled-data control systems are investigated as the last work in the thesis, which is presented in Chapter 5. In this task, the IT2 PFMB tracking control system is extended to the sampled-data based one. Through using the sampled output of both the control system and the reference system, an IT2 polynomial sampled-data based output feedback fuzzy controller can be designed to ful ll the tracking control task, the stability conditions can be obtained in terms of SOS and the tracking error is attenuated by the H1 performance index. As did in the previous two works, the information of the IT2 membership functions is used to relax the stability conditions and improve the tracking performance. The approaches proposed in the thesis to relax the stability conditions as well as to improve the tracking performance of the IT2 PFMB control systems are proved through the Lyapunov based stability theory. Meanwhile, simulation examples are provided to demonstrate and verify the theoretical analysis.
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Marrez, Jérémy. "Représentations adaptées à l'arithmétique modulaire et à la résolution de systèmes flous." Electronic Thesis or Diss., Sorbonne université, 2019. https://accesdistant.sorbonne-universite.fr/login?url=https://theses-intra.sorbonne-universite.fr/2019SORUS635.pdf.
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Les calculs modulaires entrant en jeu dans les applications en cryptographie asymétrique utilisent le plus souvent un modulo premier standardisé, dont le choix n’est pas toujours libre en pratique. L’amélioration des opérations modulaires est centrale pour l’efficacité et la sécurité de ces primitives. Cette thèse propose de fournir une arithmétique modulaire efficace pour le plus grand nombre de premiers possible, tout en la prémunissant contre certains types d’attaques. Pour ce faire, nous nous intéressons au système PMNS utilisé pour l’arithmétique modulaire, et proposons des méthodes afin d’obtenir de nombreux PMNS pour un premier donné, avec une arithmétique efficace sur les représentations. Nous considérons également la randomisation des calculs modulaires via des algorithmes de type Montgomery et Babaï en exploitant la redondance intrinsèque aux PMNS. Les changements induits de représentation des données au cours du calcul empêchent un attaquant d’effectuer des hypothèses utiles sur ces représentations. Nous présentons ensuite un système hybride, HyPoRes, avec un algorithme améliorant les réductions modulaires pour tout modulo premier. Les nombres sont représentés dans un PMNS avec des coefficients en RNS. La réduction modulaire est plus rapide qu’en RNS classique pour les premiers standardisés pour ECC. En parallèle, nous étudions un type de représentation utilisé pour la résolution réelle de systèmes flous. Nous revisitons l’approche globale de résolution faisant appel à des techniques algébriques classiques et la renforçons. Ces résultats incluent un système réel appelé la transformation réelle qui simplifie les calculs, et la gestion des signes des solutionsModular computations involved in public key cryptography applications most often use a standardized prime modulo, the choice of which is not always free in practice. The improvement of modular operations is fundamental for the efficiency and safety of these primitives. This thesis proposes to provide an efficient modular arithmetic for the largest possible number of primes, while protecting it against certain types of attacks. For this purpose, we are interested in the PMNS system used for modular arithmetic, and propose methods to obtain many PMNS for a given prime, with an efficient arithmetic on the representations. We also consider the randomization of modular computations via algorithms of type Montgomery and Babaï by exploiting the intrinsic redundancy of PMNS. Induced changes of data representation during the calculation prevent an attacker from making useful assumptions about these representations. We then present a hybrid system, HyPoRes , with an algorithm that improves modular reductions for any prime modulo. The numbers are represented in a PMNS with coefficients in RNS. The modular reduction is faster than in conventional RNS for the primes standardized for ECC. In parallel, we are interested in a type of representation used to compute real solutions of fuzzy systems. We revisit the global approach of resolution using classical algebraic techniques and strengthen it. These results include a real system called the real transform that simplifies computations, and the management of the signs of the solutions
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Agafonov, Evgeny. "Fuzzy and multi-resolution data processing for advanced traffic and travel information." Thesis, Nottingham Trent University, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.271790.
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Cook, Brandon M. "An Intelligent System for Small Unmanned Aerial Vehicle Traffic Management." University of Cincinnati / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1617106257481515.
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Sathyan, Anoop. "Intelligent Machine Learning Approaches for Aerospace Applications." University of Cincinnati / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1491558309625214.
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Muševič, Sašo. "Non-stationary sinusoidal analysis." Doctoral thesis, Universitat Pompeu Fabra, 2013. http://hdl.handle.net/10803/123809.
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Muchos tipos de señales que encontramos a diario pertenecen a la categoría de sinusoides no estacionarias. Una gran parte de esas señales son sonidos que presentan una gran variedad de características: acústicos/electrónicos, sonidos instrumentales harmónicos/impulsivos, habla/canto, y la mezcla de todos ellos que podemos encontrar en la música. Durante décadas la comunidad científica ha estudiado y analizado ese tipo de señales. El motivo principal es la gran utilidad de los avances científicos en una gran variedad de áreas, desde aplicaciones médicas, financiera y ópticas, a procesado de radares o sonar, y también a análisis de sistemas. La estimación precisa de los parámetros de sinusoides no estacionarias es una de las tareas más comunes en procesado digital de señales, y por lo tanto un elemento fundamental e indispensable para una gran variedad de aplicaciones.
Las transformaciones de tiempo y frecuencia clásicas son solamente apropiadas para señales con variación lenta de amplitud y frecuencia. Esta suposición no suele cumplirse en la práctica, lo que conlleva una degradación de calidad y la aparición de artefactos. Además, la resolución temporal y frecuencial no se puede incrementar arbitrariamente debido al conocido principio de incertidumbre de Heisenberg. \\
El principal objetivo de esta tesis es revisar y mejorar los métodos existentes para el análisis de sinusoides no estacionarias, y también proponer nuevas estrategias y aproximaciones. Esta disertación contribuye sustancialmente a los análisis sinusoidales existentes: a) realiza una evaluación crítica del estado del arte y describe con gran detalle los métodos de análisis existentes, b) aporta mejoras sustanciales a algunos de los métodos existentes más prometedores, c) propone varias aproximaciones nuevas para el análisis de los modelos sinusoidales existentes i d) propone un modelo sinusoidal muy general y flexible con un algoritmo de análisis directo y rápido.Many types of everyday signals fall into the non-stationary sinusoids category. A large family of such signals represent audio, including acoustic/electronic, pitched/transient instrument sounds, human speech/singing voice, and a mixture of all: music. Analysis of such signals has been in the focus of the research community for decades. The main reason for such intense focus is the wide applicability of the research achievements to medical, financial and optical applications, as well as radar/sonar signal processing and system analysis. Accurate estimation of sinusoidal parameters is one of the most common digital signal processing tasks and thus represents an indispensable building block of a wide variety of applications. Classic time-frequency transformations are appropriate only for signals with slowly varying amplitude and frequency content - an assumption often violated in practice. In such cases, reduced readability and the presence of artefacts represent a significant problem. Time and frequency resolu
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He, Guan-Sian, and 何冠賢. "Stability Analysis of Polynomial Fuzzy Systems." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/76065397030027969171.
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碩士國立中正大學
光機電整合工程研究所
100
This study presents a polynomial fuzzy model and a path controller design for a nonlinear four-wheeled omnidirectional mobile robot (ODMR) using polynomial fuzzy systems. A polynomial controller was designed according to the parallel distributed compensation (PDC) from the given polynomial fuzzy model of the ODMR. This proposed controller is capable of driving the closed-loop system states of the ODMR to follow reference trajectory commands. We used stability conditions that were represented by the sum of squares (SOS) to guarantee global stability. In addition, we derived the limitation conditions represented in term of SOS for control input and output using a polynomial Lyapunov function. The stable polynomial controller satisfied the constraint on the control input and output. These proposed SOS-based constraint conditions are more general and relaxed than are current linear matrix inequality (LMI)-based constraint conditions. This study focuses on developing methods for stability analysis and stabilization based on the SOS approach and that depend on the size of the time-delay. A polynomial Lyapunov function was applied to derive the stability and stabilization time-delay conditions of the nonlinear time-delay systems, and contained quadratic Lyapunov functions as a special case. Finally, computer simulations showed that the SOS-based approaches were more effective than were the LMI-based approaches.
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WU, LING-YOU, and 吳凌侑. "Robust Switching Controller Design of Polynomial Fuzzy Systems." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/f63ca9.
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碩士國立中正大學
光機電整合工程研究所
106
In this thesis, a switching polynomial Lyapunov function is proposed to be applied to design robust switching controllers for Type-1 (T1) and interval Type-2 (IT2) polynomial fuzzy systems, respectively. The switching polynomial Lyapunov function partitions the membership function into operation intervals such that the feedback gain for each subinterval can be found and relaxed stability conditions can be acquired. In addition, the robust control performance of the system can be improved by deriving the relaxed stability conditions for the system with external disturbances and model uncertainties. Therefore, based on the switching polynomial Lyapunov function, seven relaxed stability conditions in terms of sum of squares (SOS) are proposed, which are the stability conditions of the switching T1 polynomial fuzzy systems with external disturbances, the stability conditions of the switching T1 polynomial fuzzy systems with model uncertainties, the robust stability conditions of the switching T1 polynomial fuzzy systems with external disturbances and model uncertainties, the stability conditions of the switching IT2 polynomial fuzzy systems, the stability conditions of the switching IT2 polynomial fuzzy systems with external disturbances, the stability conditions of the switching IT2 polynomial fuzzy systems with model uncertainties, and the robust stability conditions of the switching IT2 polynomial fuzzy systems with external disturbances and model uncertainties, respectively. Then computer simulations are carried out through two polynomial fuzzy model Examples to verify the effectiveness of the proposed robust controller against external disturbances and model uncertainties. Finally, the Theorems proposed in this thesis are realized by the tracking control experiments of the wheeled mobile robot (WMR).
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HUANG, RUEY-SHENG, and 黃瑞盛. "Switching Polynomial Fuzzy Networked Control Systems of Mobile Robots." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/kx97h3.
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碩士國立中正大學
光機電整合工程研究所
107
This paper discusses the design of a switching polynomial fuzzy network control system, which are applied to the type-1 (T1) and interval type-2 (IT2) polynomial fuzzy networked controller by using the switching polynomial Lyapunov-Krasovskii function. The switching polynomial Lyapunov-Krasovskii function is composed of multiple local polynomial Lyapunov functions, which can expand the feasible region through relaxing stability conditions, so that the performance of the controller is better. Therefore, based on the switching polynomial Lyapunov-Krasovskii function, eight relaxed stability conditions in terms of sum of squares (SOS) are proposed, which are the stability conditions of switching T1 polynomial fuzzy networked control systems, the stability conditions of switching T1 polynomial fuzzy networked control systems with external disturbances, the stability conditions of switching T1 polynomial fuzzy networked control systems with model uncertainties, the robust stability conditions of switching T1 polynomial fuzzy networked control systems with external disturbances and model uncertainties, the stability conditions of switching IT2 polynomial fuzzy networked control systems, the stability conditions of switching IT2 polynomial fuzzy networked control systems with external disturbances, the stability conditions of switching IT2 polynomial fuzzy networked control systems with model uncertainties, the robust stability conditions of switching IT2 polynomial fuzzy networked control systems with external disturbances and model uncertainties. These stability conditions also consider the time delay and packet dropout caused by network control. Then a simulation is performed through a single-rigid robot and polynomial fuzzy models to verify the validity of the proposed theorem applied to the controller against external disturbances and model uncertainties. Finally, the wheeled mobile robot controller design is used for tracking control experiments to achieve the superiority of the theorem proposed in this paper.
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Wang, Shun-Min, and 王舜民. "Output-Feedback Control of Networked Nonlinear Systems: Polynomial Fuzzy Approach." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/50396743892611438077.
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碩士國立中正大學
光機電整合工程研究所
101
This study makes use of the polynomial fuzzy approach for output-feedback control in networked control systems (NCSs) that are subject to external disturbances and model uncertainties, taking into account, the issues of network-induced delay and packet dropout in NCSs. A novel output feedback polynomial fuzzy controller design is proposed for nonlinear NCSs which are with external disturbances and model uncertainties. The authors utilized Lyapunov-Krasovskii functionals and the criterion to derive a theorem for robust stability conditions based on sum of squares (SOS), which can be numerically solved using the Matlab toolbox SOSTOOLS. The results of the simulations are provided to illustrate effectiveness of the static output feedback polynomial fuzzy controller design.
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Sung, Tin-Wen, and 宋廷文. "Sampled-Data Tracking Control for Polynomial Fuzzy Time-delay Systems." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/8xr269.
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碩士國立臺北科技大學
自動化科技研究所
105
The H∞ sampled-data tracking control problem for polynomial fuzzy time-delay system is investigated in this thesis. The sampled-data state feedback and output feedback tracking controllers for polynomial fuzzy time-delay system are proposed to stabilize the polynomial fuzzy time-delay system state and drive it to follow those of a stable reference model subject to an H∞ performance. In addition, based on the Lyapunov theorem, the sum-of-squares-based stabilization conditions are obtained to guarantee the stability of the polynomial fuzzy time-delay system and facilitate the controller synthesis. Lastly, four examples are illustrated to show the effectiveness and feasibility of the proposed results.
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Huang, Yu-Chia, and 黃宥嘉. "Intelligent Robust H∞ Control of Polynomial Fuzzy Systems Using QEA." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/ctmb2y.
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博士國立臺灣海洋大學
電機工程學系
105
This dissertation investigates polynomial fuzzy control systems and proposes several polynomial fuzzy controllers, including stable controller design, robust H∞ controller design, intelligent controller design, and intelligent robust H∞ controller design. System stability is analyzed using a non-quadratic Lyapunov function, and stability conditions based on the sum-of-squares (SOS) are proposed. The control gains are obtained by solving these stability conditions using numerical analysis software such as SOSTOOLS. In the study of stable controller design, methods of changing the response speed of the system are discussed, and a controller is designed to limit the output and present the decay-rate-index-based stability conditions and output constraints. In order to ensure robustness to external disturbances and model uncertainties, this dissertation presents robust H∞ controller design methods. First, polynomial fuzzy control systems, which can describe model uncertainties and external disturbances, are proposed for continuous-time and discrete-time nonlinear systems. The robust H∞ conditions are derived using the H∞ criterion and non-quadratic Lyapunov function to analyze system stability. In order to improve the performance of the stable controller and the robust H∞ controller, a method combining the quantum-inspired evolutionary algorithm (QEA) and SOS-based stability conditions is presented, and an intelligent controller and intelligent robust H∞ controller design are presented. In this method, QEA adopts the SOS-based stability conditions to guarantee system stability during the control gains search procedure. Accordingly, the optimal control gain, which is satisfied with the performance requirements, will be screened out. In addition, to enhance the probability of complying with the SOS-based stability conditions, the polynomial Lyapunov function is used to analyze closed-loop system stability, and relaxed stability and relaxed robust H∞ stability conditions are derived. Several simulations demonstrate the effectiveness and feasibility of each proposed method.
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Cheng, Yu-Hsuan, and 鄭宇軒. "SOS-based Switching Control for Discrete-Time Polynomial Fuzzy Systems." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/578u6h.
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碩士國立中正大學
光機電整合工程研究所
106
In this thesis, the switching polynomial Lyapunov function is proposed to be applied to the switching control of discrete-time polynomial fuzzy systems. The switching polynomial Lyapunov function cuts the membership functions into several operation subspaces to find the feedback gain of each operation subspaces such that the system stability conditions are relaxed. This thesis also considers the influences of external disturbance and model uncertainty to derive the sum-of-squares (SOS)-based stability conditions of discrete-time switching polynomial fuzzy control systems. In this thesis, eight theorems are proposed, which are the basic stability theorem for discrete-time type-1 switching polynomial fuzzy control systems (DT1SPFCS), the H∞ stability theorem for DT1SPFCS with external disturbance, the robust stability theorem for DT1SPFCS with model uncertainty, the robust H∞ stability theorem for DT1SPFCS with external disturbance and model uncertainty, the basic stability theorem for discrete-time interval type-2 switched polynomial fuzzy control systems (DIT2SPFCS), the H∞ stability theorem for DIT2SPFCS with external disturbance, the robust stability theorem for DIT2SPFCS with model uncertainty, and the robust H∞ stability theorem for DIT2SPFCS with external disturbance and model uncertainty, respectively. In addition, several computer simulations are given to verify the effectiveness of the proposed theorems, and the number of operation subspaces, the partition way of membership functions, and the feasible space of stability conditions are studied. Finally, the discrete-time switching polynomial fuzzy control systems proposed in this thesis are applied to the path tracking of a wheeled mobile robot (WMR), and compared with the existing literature, the superiority of the proposed method is revealed.
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Lin, Yu-Hsin, and 林侑欣. "Design and Implementation of a Bidirectional Converter Using Polynomial Fuzzy Systems." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/244wf7.
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碩士國立中正大學
電機工程研究所
102
The main purpose of this study is to present the design and implementation of a bidirectional converter using polynomial fuzzy systems. The topology of this circuit is combined the buck converter with the boost converter. Its two most pleasing traits are high efficiency and low cost. In this circuit, the microprocessor, TMS320F28069, realizes almost all of the functions, such as circuit protection, generation of pulse-width modulation (PWM) signals and A/D conversion, etc. This study uses Lyapunov function to derive a theorem of uncertainty stability conditions based on polynomial fuzzy. And, it uses SOSTOOLS to fine the control gain of systems. Finally, a 2 kW bidirectional converter using polynomial fuzzy system had been implemented and added Lithium-ion battery to verify the feasibility and characteristic systems.
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Chang, Chih-Heng, and 張智恆. "Robust H∞ Design for Networked Control Systems Using Polynomial Fuzzy Model." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/68970602623955482219.
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碩士國立中正大學
光機電整合工程研究所
101
This paper investigates robust H∞ design for continuous-time polynomial fuzzy networked control systems (NCSs) with external disturbances and model uncertainties, taking into account the network-based environment issues of the network-induced delay and packet dropout. Using polynomial Lyapunov function, robust stability conditions for polynomial fuzzy NCSs are derived, which possess H∞ performance and are expressed in terms of sum of squares (SOS). A H∞ polynomial fuzzy controller is developed for the stabilization of NCSs and to attenuate the influence of external disturbances and model uncertainties in practical applications. Finally, numerical simulations based on TrueTime toolbox are conducted in order to illustrate the robust performance and effectiveness of the proposed approach.
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Lin, Chung-Yen, and 林忠諺. "Robust H∞ Control of Polynomial Fuzzy Systems: Piecewise Lyapunov Function Approach." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/4g658n.
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碩士國立中正大學
光機電整合工程研究所
106
In this thesis, the switching polynomial fuzzy controller is designed by the piecewise polynomial Lyapunov function (PPLF) and applied to the type-1 (T1) and interval type-2 (IT2) polynomial fuzzy models. Through the characteristics of the minimum-type PPLF, the SOS-based stability conditions can be more relaxed. Therefore, this thesis proposes six stability theorems for polynomial fuzzy control systems (PFCS) by using the PPLF, which are SOS-based H∞ stability conditions for T1 PFCS with external disturbance, SOS-based robust H∞ stability conditions for T1 PFCS with both external disturbance and model uncertainty, SOS-based stability conditions for IT2 PFCS, SOS-based H∞ stability conditions for IT2 PFCS with external disturbance, SOS-based robust stability conditions for IT2 PFCS with model uncertainty, and SOS-based robust H∞ stability conditions for IT2 PFCS with both external disturbance and model uncertainty, respectively. Then through computer simulations, it is verified that the proposed stability conditions are more relaxed than the existing stability conditions. Finally, the designed switching polynomial fuzzy controller is applied to a wheeled mobile robot (WMR), which shows that it owns better response performance.
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Chiu, Chieh-wei, and 邱价偉. "Controller Design for Polynomial Fuzzy Bilinear Systems via Homogeneous Lyapunov Methods." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/s83e69.
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碩士國立中央大學
機械工程學系
107
The main contribution in this thesis is a state feedback controller design for polynomial fuzzy bilinear systems modeled by Taylor series. The stability is proved with homogeneous polynomial Lyapunov function. In this thesis, two methods to tackle the control problem of polynomial fuzzy bilinear systems are proposed. In the first method we combine the bilinear term Nxu into the Bu term. The second method is to describe control input with trigonometric functions. For continuous-time systems, we utilize the Euler's homogeneous polynomial theorem to solve the V(x) which is created by time derivative of V(x), and build the homogeneous Lyapunov function.In discrete-time systems, the non-homogeneous Lyapunov function state x is a collection of system states that are unaffected by control. This restriction is to avoid problems when doing simulation. The details will be described in this thesis. Finally in numerical simulations, we test the stability condition of the fuzzy systems via Sum Of Squares, and design the state feedback controllers.
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Pan, Chia-Min, and 潘家民. "Polynomial Fuzzy Observed-Based Output Feedback Control for Nonlinear Hyperbolic PDE Systems." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/9djkzk.
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碩士國立臺北科技大學
自動化科技研究所
106
This thesis investigates the output feedback control problem for the nonlinear hyperbolic partial differential equations (PDEs) system. Firstly, by utilizing the Taylors series identification approach, the nonlinear hyperbolic PDEs model can be represented by the polynomial fuzzy PDE model. For the controller design, three different types of state estimation and control design problems for polynomial fuzzy PDE system are explored. By examining the stabilization problem, the Eulers relation, polynomial Lyapunov-Krasovskii functional and sum-of-squares approach are adopted and the exponential stabilization condition is formulated in terms of the spatial derivative sum-of-squares (SDSOS). Lastly, a hyperbolic PDE system and some numerical examples are provided to illustrate the effectiveness and validity of the proposed design method.
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Li, Zhuo-Rui, and 李卓叡. "SOS-based Robust Control of Discrete-Time Interval Type-2 Polynomial Fuzzy Systems." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/8n65mm.
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碩士國立中正大學
光機電整合工程研究所
103
In this thesis, four SOS (sum of squares)-based theorems are used to design a robust controller for discrete-time IT2 (interval type-2) polynomial fuzzy systems. IT2 fuzzy sets are used to construct membership functions of these polynomial fuzzy models and controllers. According to whether the system involves external disturbance or model uncertainty for four kinds of cases, the sum of square stability condition for the discrete-time IT2 polynomial fuzzy control systems by polynomial Lyapunov faction is derived. First is the stability theorem, applied without taking into account external disturbances and model uncertainty for the discrete-time IT2 polynomial FCSs. Second is the proposed H∞ stability theorem for discrete-time IT2 polynomial FCSs involving external disturbances. The fourth theorem is the robust stability theorem for discrete-time IT2 polynomial FCSs involving both external disturbances and model uncertainty. The benefits of these four kinds of discrete-time IT2 polynomial fuzzy controllers can be achieved by SOSTOOLS, solving the proposed stability conditions. Simulation results illustrate the SOS-based discrete-time IT2 polynomial fuzzy controllers achieve excellent performance compared with discrete-time T1 polynomial fuzzy controllers, and verify that the SOS-based robust stability conditions are more general.
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CHEN, XUE-CHENG, and 陳學呈. "Design and Implementation of Three-Phase Bidirectional Inverter Based on Polynomial Fuzzy Systems." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/59ug7d.
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Lin, Jing-Ru, and 林璟儒. "Robust Design for Networked Control Systems Using Interval Type-2 Polynomial Fuzzy Model." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/87431883952817322052.
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碩士國立中正大學
光機電整合工程研究所
104
This work provides stability conditions for interval type-2 polynomial fuzzy network control systems and proposes a new interval type-2 polynomial fuzzy logic network control theorem. The theorem considers two problems of network control systems: packet loss and network delay. Robust and stable interval type-2 polynomial fuzzy network control systems can resist packet loss and network delay by using Lyapunov-Krasovskii functional with a sum of squares approach. This study reports results from a simulated network environment to confirm the effectiveness of the interval type-2 polynomial fuzzy network controller and to describe the feasible region in terms of the theorem. A physical robot network control experiment provided results that verified the practicability of implementation.
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Lin, Feng-yi, and 林峯億. "Stabilization Analysis of Polynomial Fuzzy Systems via SOS - Euler's Theorem for Homogeneous Functions." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/73298007740545955191.
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碩士國立中央大學
機械工程學系
101
Extension of the state dependent Riccati inequalities to non-quadratic Lyapunov function of the form V(x) = 1/2(x^TP^(-1)(x)x), with P^(-1)(x) > 0 requires that P(x)x is a gradient of positive definite function. Unfortunately, the test of P^(-1)(x)x is nonconvex problem. Thus this thesis studies stabilization problems of the polynomial fuzzy systems via homogeneous Lyapunov functions exploiting the Euler’s homogeneity property and algebraic property of Pólya to construct a family of SOS polynomials that solves the nonconvexity problem and releases conservatism as well. Lastly, examples of polynomial fuzzy systems are demonstrated to show the proposed method being effective and effective.
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Liang, En-Chen, and 梁恩晟. "Switching Static Output Feedback Controller for Polynomial Fuzzy Systems via Homogeneous Lyapunov Functions." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/t4367f.
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碩士國立中央大學
機械工程學系
107
In this paper, we study switching static output feedback control problem for both continuous- and discrete-time polynomial fuzzy systems. The stabilization of the systems is proved with minimum-type piecewise Lyapunov functions, which have the form V(x)=\min_{1\leq l \leq N}\big\{V_l(x)\big\}. Switching mechanism of the controllers is also based on piecewise Lyapunov functions. In continuous-time systems, in order to remove non-convex term \dot P(x), via Euler's theorem for homogeneous functions we establish piecewise functions as follows. V_l(x)=x^TP_l(x)x=\frac{1}{g(g-1)}x^T\nabla_{xx}V_l(x)x In discrete-time systems, the piecewise functions are defined as V_l(x)=x^TP_l^{-1}(\tilde x)x$ to prevent problems where \tilde x is the set of states whose corresponding row in B_i(x) are empty. Further details are described in the text. In numerical examples, stability conditions and controller synthesis are tested and solved via sum-of-squares approach.
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Liu, Chun-Lin, and 劉俊麟. "Inconsistency Resolution and Rule Insertion of Fuzzy Rule-Based Systems." Thesis, 1997. http://ndltd.ncl.edu.tw/handle/82933815705848511659.
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碩士國立台灣工業技術學院
電子工程技術研究所
85
In this paper, a fuzzy rule inconsistency resolution and insertion method is proposed on a fuzzy neural network, named Knowledge-Based Neural Network with Trapezoid Fuzzy Set inputs (KBNN/TFS). To facilitate the processing of fuzzy information, LR-fuzzy interval is employed. Necessity support and possibility support (named support pair) are applied to detect and remove inconsistency. In addition to the support pair, the concept of initial learning point is used to handle rule insertion. We show the works of the proposed methods on an example named Knowledge Base Evaluator (KBE). After inconsistency resolution operations, inconsistencies are resolved, and the learning result is improved. Moreover, to set initial learning point on deleted conflict rule, a new rule isgenerated and inserted to the system. And the result is much better than only applying inconsistency resolution.
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LIU, PEI-YEN, and 劉沛彥. "Output-Feedback Control of Networked Nonlinear Control Systems: Interval Type-2 Polynomial Fuzzy Approach." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/vu75q3.
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碩士國立中正大學
機電光工程研究所
104
This thesis investigates the effectiveness of using an interval type-2 (IT2) polynomial fuzzy control approach for designing output feedback networked control systems (NCSs) when package dropout, time delay, external disturbance, model uncertainties are considered simultaneously. In the process of controller design, the model uncertainties are modified in IT2 fuzzy sets with upper-bound and lower-bound membership functions, and the H∞ performance index is introduced to address the problem of disturbance rejection. Moreover, package dropout and time delays can be mitigated by applying the proposed IT2 sum-of-squares (SOS)-based robust conditions derived from the Lyapunov–Krasovskii functional. In addition, this thesis proposes additional relaxed SOS stability conditions for increasing the number of feasible solutions. The simulation results demonstrate that the proposed IT2 polynomial fuzzy approach outperforms the type-1 polynomial fuzzy approach. Finally, a wireless wheel mobile robot was controlled via internet to verify the proposed theorem.
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Huang, Guan-Fu, and 黃冠福. "Design of SOS-based Robust Controller for Interval Type-2 Polynomial Fuzzy Logic Control Systems." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/g3q82d.
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碩士國立中正大學
光機電整合工程研究所
103
This thesis presents an application of an interval type-2 (IT2) fuzzy logic system to construct a polynomial fuzzy model and design an IT2 polynomial fuzzy controller. The IT2 fuzzy logic system was used because of its greater robustness against model uncertainty compared with type-1 (T1) fuzzy logic systems. A polynomial fuzzy control system (FCS) enables representing a state matrix with a polynomial, substantially reducing the number of fuzzy rules. Therefore, this thesis presents four theorems for IT2 polynomial FCS stability conditions: sum of squares (SOS)-based stability condition for designing an IT2 polynomial FCS involving decay rates, SOS-based stability condition for designing an IT2 polynomial FCS involving external disturbances, SOS-based stability condition for an IT2 polynomial FCS by assessing model uncertainty, and SOS-based stability condition for an IT2 polynomial FCS involving both external disturbances and model uncertainty. Finally, the results compared with the examples of Tanaka and Lam confirmed that the proposed IT2 polynomial fuzzy control system was more relaxed and general compared with a traditional T1 polynomial fuzzy control system.
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LIU, CHIA-YU, and 劉家侑. "Design and Implementation of a Single-Phase Bidirectional Inverter Using Robust Polynomial Fuzzy Control Systems." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/29621161594481688113.
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碩士國立中正大學
電機工程研究所
104
In this thesis, the robust polynomial fuzzy control system are applied to a 2kW single-phase bidirectional inverter, which can operate on rectification mode and grid-connection mode. First the state-space equation of the single-phase bidirectional inverter is derived. The state variable of the integration of error is introduced to argument the state-space model. As a result, the nonlinear state equation of the inverter can be formulated via the polynomial fuzzy model. By adopting the Lyapunov stability theorem, the stability conditions for the inverter control system are propose such that the bias of diodes, voltage drop of power switches, and internal impedance of elements are restrained. These stability conditions are presented in the form of sum of squares. The control stage circuit is designed and implement, which includes the function of voltage drop feedback, LCD display and PWM signals output. The robust polynomial fuzzy controller is realized by the microprocessor TMS320F28069. Since the inductance variation has been considered in the design of the proposed polynomial fuzzy controller, there is no need to load the inductance data into the microprocessor. Compared to the division-summation method, the computation burden can be alleviated in the chip. Both computer simulation and experimental results demonstrate that the propose robust polynomial fuzzy controller is superior to the division-summation controller for the single-phase bidirectional inverter with external disturbance and model uncertainty operated on grid-connection mode and rectification mode.
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Fang, Cone-Jie, and 方琮傑. "Relaxed Stabilization Conditions Analysis for T-S Fuzzy Systems with Time-Delay: A Homogeneous Polynomial Approach." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/s2fzq6.
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碩士國立臺北科技大學
自動化科技研究所
102
There are two parts in this thesis. In the first part, based on the delay-dependent Lyapunov function and homogenous polynomial technique, the stabilization condition is proposed for T-S fuzzy system with time-delay. In addition, by examining the relaxed stabilization condition, Pólya theorem and slack matrix variables are adopted to reduce the conservative of the proposed stabilization condition. Moreover, some examples are borrowed from the existing studies to demonstrate that the proposed method can provide the maximal allowable delay time than the other studies. In the second part, the stabilization condition for discrete-time T-S fuzzy system with time-delay is explored. By utilizing the weighting-dependent Lypunov function and weighting-matrix method, the conservatism of stabilizations are reduced. Lastly, some numerical examples are illustrated to demonstrate that the proposed relaxed stabilization conditions can provide the maximal allowable delay-time than some studies.
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CHU, CHENG-TAI, and 朱承泰. "Design and Implementation of Three-Phase Bidirectional Inverter Based on Interval Type-2 Polynomial Fuzzy Control Systems." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/b34vb4.
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碩士國立中正大學
電機工程研究所
106
A three-phase bidirectional inverter based on interval type-2 polynomial fuzzy control systems is designed and implemented in this thesis. The microcontroller Renesas RX62T is implemented as the system core. The systems parameters are feedbacked to the interval type-2 polynomial fuzzy controller via peripheral circuits and analog-to-digital converter (ADC). After calculations, the duty ratios of power switches in corresponding interval are obtained. This system can be operated in grid-connected mode and rectification mode. In this thesis, the state equation of three-phase inverter is first derived from two phase modulation (TPM). Next, the sum of square (SOS) type stability equation of the interval type-2 fuzzy control system with disturbance suppression is derived according to the Lyapunov stability theorem. The controller is designed based on the parallel distributed compensation(PDC) method. And the controller gain is solved by the SOS Toolbox. Finally, the control performance is verified by experimental results.
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LIN, SHENG-BIN, and 林聖斌. "Design and Implementation of a Single-Phase Bidirectional Inverter Using Robust Polynomial Fuzzy Output-Feedback Tracking Control Systems." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/rsdbt6.
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HSIEH, MENG-HSUEH, and 謝孟學. "Design and Implementation of a Single-Phase Bidirectional Inverter Using IT2 Polynomial Fuzzy Output-Feedback Tracking Control Systems." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/htc643.
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碩士國立中正大學
電機工程研究所
106
This thesis designs an interval type-two (IT2) polynomial fuzzy output-feedback tracking controller and applies it to a single-phase bidirectional inverter with 2 kW power rating. First, the architecture and the circuit operation principle of the single-phase bidirectional inverter are introduced. The equation of state and the voltage regulation mechanism of DC microgrids are derived for the rectification mode and the grid connection mode, respectively. The design of the control systems is based on the Lyapunov stability theory, and two stability theorems of the IT2 polynomial fuzzy output-feedback tracking control systems are proposed. The SOS (Sum of Squares) stability conditions in Theorem1 tolerate the uncertainties of the premise parameters and consider external disturbances. In addition to the advantages of Theorem 1, Theorem 2 also considers the real situation of non-ideal circuits, including the model uncertainties due to parameter variations and component aging. Therefore, the SOS stability conditions in Theorem 2 owns robust performance. Finally, the single-phase bidirectional inverter with the IT2 polynomial fuzzy output-feedback tracking control systems is applied to perform computer simulation and experiments in the rectification mode and the grid connection mode, such as 1 kW, 1.5 kW, 2 kW, robustness and linear voltage regulation. By replacing the inductor and adding external disturbances, it is verified that the proposed control systems possess the robustness to tolerate model uncertainties and suppress external disturbances. When the load changes, the DC voltage can be adjusted and maintained within the set range. Comparing simulations and experimental results shows that the single-phase bidirectional inverter developed in this thesis has excellent control performance whether it is operated in rectification mode or grid connection mode.
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Li, Jui-Chan, and 李睿展. "Design and Implementation of a Maximum Power Point Tracker for PV Arrays Based on Robust Polynomial Fuzzy Control Systems." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/bprm9q.
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CHIANG, YA-HSUAN, and 蔣亞軒. "Design and Implementation of a Bidirectional Converter Using Interval Type-2 Robust Polynomial Fuzzy Systems with Time-Delay Dependent." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/36kx76.
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CHEN, JYUN-YAN, and 陳俊晏. "Design and Implementation of a Three-Phase Bidirectional Inverter Using Finite-Time Polynomial Fuzzy Output-Feedback Tracking Control Systems." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/ra5e4s.
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碩士國立中正大學
電機工程研究所
107
This thesis designs a finite-time polynomial fuzzy output-feedback tracking control which is applied to a 5 kW three-phase bidirectional inverter. First, the circuit architecture of a three-phase bidirectional inverter is introduced. Because the system can operate in rectification mode and grid-connection mode, the state-equations in the two modes can be derived according to two-phase modulation (TPM), and we propose two theorems based on the finite-time polynomial fuzzy output-feedback tracking control. Theorem 1 has the Hꝏ performance which can restrain external disturbances to make the system stable in transient time, and we propose the SOS (Sum of Squares) stability equations. Theorem 2 has not only the advantages of theorem 1, but also considers the aging of components. Theorem 2 is more robust than theorem 1, so it also has the SOS stability equations to satisfy theorem 2 of stability conditions. Theorems 1 and 2 get the gains of the finite-time polynomial fuzzy output-feedback tracking control using Matlab SOSTOOLS. Finally, the gains are applied to three-phase bidirectional inverter, and operated in rectification mode and grid-connection mode. Experiments contain the constant power, such as 1kW, 3kW, 5kW, robustness of simulation and measurements. The results demonstrate that the performance of the Three-Phase bidirectional inverter using finite-time polynomial fuzzy output-feedback tracking controller is better than that of the division-summation controller for the three-phase bidirectional Inverter.
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MING-DE, YANG, and 顏銘德. "Design and Implementation of a Maximum Power Point Tracker for PV Arrays Based on Non-PDC Robust Polynomial Fuzzy Control Systems." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/a2jyke.
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