Robust Multi-Criteria Optimal Fuzzy Control of Continuous-Time Nonlinear Systems

This paper presents a novel fuzzy control design of continuous-time nonlinear systems with multiple performance criteria. The purpose behind this work is to improve the traditional fuzzy controller performance to satisfy several performance criteria simultaneously to secure quadratic optimality with inherent stability property together with dissipativity type of disturbance reduction. The Takagi– Sugeno fuzzy model is used in our control system design. By solving the linear matrix inequality at each time step, the control solution can be found to satisfy the mixed performance criteria. The effectiveness of the proposed technique is demonstrated by simulation of the control of the inverted pendulum system

Control design for discrete-time fuzzy systems with disturbance inputs via delta operator approach

This paper is concerned with the problem of passive control design for discrete-time Takagi-Sugeno (T-S) fuzzy systems with time delay and disturbance input via delta operator approach. The discrete-time passive performance index is established in this paper for the control design problem. By constructing a new type ofLyapunov-Krasovskii function (LKF) in delta domain, and utilizing some fuzzy weighing matrices, a new passive performance condition is proposed for the system under consideration. Based on the condition, a state-feedback passive controller is designed to guarantee that the resulting closed-loop system is very-strictly passive. The existence conditions of the controller can be expressed by linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate the feasibility and effectiveness of the proposed method

Dynamic output-feedback passivity control for fuzzy systems under variable sampling

This paper concerns the problem of dynamic output-feedback control for a class of nonlinear systems with nonuniform uncertain sampling via Takagi-Sugeno (T-S) fuzzy control approach. The sampling is not required to be periodic, and the state variables are not required to be measurable. A new type fuzzy dynamic output-feedback sampled-data controller is constructed, and a novel time-dependent Lyapunov-Krasovskii functional is chosen for fuzzy systems under variable sampling. By using Lyapunov stability theory, a sufficient condition for very-strict passive analysis of fuzzy systems with nonuniformuncertain sampling is derived. Based on this condition, a novel fuzzy dynamic output-feedback controller is designed such that the closed-loop system is very-strictly passive. The existence condition of the controller can be solved by convex optimization approach. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method

Nonlinear Control and Estimation with General Performance Criteria

This dissertation is concerned with nonlinear systems control and estimation with general performance criteria. The purpose of this work is to propose general design methods to provide systematic and effective design frameworks for nonlinear system control and estimation problems. First, novel State Dependent Linear Matrix Inequality control approach is proposed, which is optimally robust for model uncertainties and resilient against control feedback gain perturbations in achieving general performance criteria to secure quadratic optimality with inherent asymptotic stability property together with quadratic dissipative type of disturbance reduction. By solving a state dependent linear matrix inequality at each time step, the sufficient condition for the control solution can be found which satisfies the general performance criteria. The results of this dissertation unify existing results on nonlinear quadratic regulator, Hinfinity and positive real control. Secondly, an H2-Hinfinity State Dependent Riccati Equation controller is proposed in this dissertation. By solving the generalized State Dependent Riccati Equation, the optimal control solution not only achieves the optimal quadratic regulation performance, but also has the capability of external disturbance reduction. Numerically efficient algorithms are developed to facilitate effective computation. Thirdly, a robust multi-criteria optimal fuzzy control of nonlinear systems is proposed. To improve the optimality and robustness, optimal fuzzy control is proposed for nonlinear systems with general performance criteria. The Takagi-Sugeno fuzzy model is used as an effective tool to control nonlinear systems through fuzzy rule models. General performance criteria have been used to design the controller and the relative weighting matrices of these criteria can be achieved by choosing different coefficient matrices. The optimal control can be achieved by solving the LMI at each time step. Lastly, since any type of controller and observer is subject to actuator failures and sensors failures respectively, novel robust and resilient controllers and estimators are also proposed for nonlinear stochastic systems to address these failure problems. The effectiveness of the proposed control and estimation techniques are demonstrated by simulations of nonlinear systems: the inverted pendulum on a cart and the Lorenz chaotic system, respectively

Variance and Passivity Constrained Fuzzy Control for Nonlinear Ship Steering Systems with State Multiplicative Noises

The variance and passivity constrained fuzzy control problem for the nonlinear ship steering systems with state multiplicative noises is investigated. The continuous-time Takagi-Sugeno fuzzy model is used to represent the nonlinear ship steering systems with state multiplicative noises. In order to simultaneously achieve variance, passivity, and stability performances, some sufficient conditions are derived based on the Lyapunov theory. Employing the matrix transformation technique, these sufficient conditions can be expressed in terms of linear matrix inequalities. By solving the corresponding linear matrix inequality conditions, a parallel distributed compensation based fuzzy controller can be obtained to guarantee the stability of the closed-loop nonlinear ship steering systems subject to variance and passivity performance constraints. Finally, a numerical simulation example is provided to illustrate the usefulness and applicability of the proposed multiple performance constrained fuzzy control method

A survey on gain-scheduled control and filtering for parameter-varying systems

Copyright © 2014 Guoliang Wei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.This paper presents an overview of the recent developments in the gain-scheduled control and filtering problems for the parameter-varying systems. First of all, we recall several important algorithms suitable for gain-scheduling method including gain-scheduled proportional-integral derivative (PID) control, H 2, H ∞ and mixed H 2 / H ∞ gain-scheduling methods as well as fuzzy gain-scheduling techniques. Secondly, various important parameter-varying system models are reviewed, for which gain-scheduled control and filtering issues are usually dealt with. In particular, in view of the randomly occurring phenomena with time-varying probability distributions, some results of our recent work based on the probability-dependent gain-scheduling methods are reviewed. Furthermore, some latest progress in this area is discussed. Finally, conclusions are drawn and several potential future research directions are outlined.The National Natural Science Foundation of China under Grants 61074016, 61374039, 61304010, and 61329301; the Natural Science Foundation of Jiangsu Province of China under Grant BK20130766; the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning; the Program for New Century Excellent Talents in University under Grant NCET-11-1051, the Leverhulme Trust of the U.K., the Alexander von Humboldt Foundation of Germany

Control of nonlinear systems using n-fuzzy models

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia de Automação e Sistemas, Florianópolis, 2015.A utilização de modelos fuzzy Takagi-Sugeno (T-S) tem sido extensivamente investigada no decorrer das últimas décadas, principalmente por propiciarem o desenvolvimento de metodologias de projeto de sistemas de controle não lineares que possuem caráter sistemático e solução numérica, fazendo-se uso de propriedades inerentes como a de aproximação universal e/ou de convexidade dos modelos. Nota-se, entretanto, que as técnicas de modelagem fuzzy T-S atuais, em geral, garantem a convexidade do modelo e/ou a sua precisão de representação somente para uma determinada região do espaço de estados. Desta forma, para estratégias de controle baseadas em propriedades de convexidade, a estabilidade do sistema de malha fechada formado pelo sistema não linear realimentado pela lei de controle fuzzy deve ser estudada no contexto de estabilidade local, sendo fundamental a determinação de regiões de estabilidade para o sistema de malha fechada. Esta importante característica dos modelos fuzzy T-S raramente é considerada na literatura, podendo implicar em perda de desempenho e até mesmo instabilidade do sistema em malha fechada. Outro problema inerente à utilização de modelos fuzzy T-S diz respeito ao aumento exponencial de complexidade do modelo com o número de não linearidades presentes no sistema, principalmente quando se busca descrever de forma exata a dinâmica do sistema a controlar, o que implica no aumento da complexidade numérica dos algoritmos para análise e projeto, assim como do aumento da complexidade de implementação de leis de controle. Neste contexto, esta tese busca evidenciar a importância da consideração da validade regional dos modelos fuzzy de tipo T-S para o desenvolvimento de ferramentas de análise e síntese de sistemas de controle não lineares, assim como considerar outras restrições físicas presentes no sistema de controle como limites nos atuadores, e discutir a problemática associada à complexidade dos modelos fuzzy T-S. Um método de modelagem baseado no uso de regras não lineares locais é desenvolvido permitindo, além de uma representação compacta e precisa da planta não linear original, o tratamento do problema de projeto de controladores dinâmicos por realimentação de saídas na presença de não linearidades dependentes de estados não mensuráveis do sistema. Utilizando-se funções de Lyapunov fuzzy (FLF), são desenvolvidas condições de estabilidade e estabilização para o sistema em malha fechada que podem ser verificadas em termos de factibilidade de um conjunto de desigualdades matriciais lineares. Os controladores propostos são baseados na realimentação de estados e do vetor de não linearidades de setor, ao qual são consideradas perturbações limitadas em energia ou amplitude, e na realimentação dinâmica de saídas, para sistemas não perturbados com atuadores saturantes ou para sistemas sujeitos a perturbações persistentes. Exemplos numéricos são apresentados ao longo do trabalho com o objetivo de ilustrar a eficiência dos métodos propostos. Ainda, objetivando auxiliar estudantes, engenheiros e pesquisadores na análise e projeto de controle de sistemas não lineares, apresenta-se o desenvolvimento de uma ferramenta computacional interativa para a modelagem e controle fuzzy. Aspectos práticos e um estudo da complexidade de implementação digital de controladores fuzzy também são discutidos através da simulação Hardware-in-the-Loop (HIL) com utilização de uma placa de desenvolvimento FPGA (do inglês Field Programmable Gate Array).Abstract : Takagi-Sugeno (T-S) fuzzy models have been extensively investigated over the last decade to develop the so-called fuzzy model based (FMB) control techniques, providing nonlinear control design methodologies with a systematic aspect and numerical solution. However, the actual T-S fuzzy modeling techniques, in general, only guarantee the convexity of the model and/or their accuracy of representation for a specific domain of the state space. Thus, for control strategies based on convexity properties, the stability of the closed-loop system composed of the nonlinear system and the fuzzy controller should be analyzed in a local context, being fundamental to determining stability regions for the closed-loop system. This inherent local characteristic is often not considered in most FMB control design results, which may lead to poor performance or even instability of the closed-loop system. In this sense, this thesis aims to consider the regional validity of the T-S fuzzy models for the development of nonlinear control systems analysis and design tools, to consider other physical constraints and to discuss the problems associated with the complexity of T-S fuzzy models. A modeling method based on the use of nonlinear local rules that provides a compact and accurate representation is presented, allowing also to handle with the dynamic output feedback control problem for systems with nonlinearities that may depend on unmeasurable states. Using fuzzy Lyapunov functions (FLF), closed-loop stability conditions are provided, which can be verified in terms of the feasibility of a set of linear matrix inequalities (LMIs). The proposed controllers are based on a state and sector nonlinearities feedback, for systems subject to disturbances bounded in energy or amplitude, and on a dynamic output feedback, for systems with saturating actuators. Numerical examples are presented throughout this document to illustrate the effectiveness of the proposed design methodologies. Further, aiming to assist students and engineers in the nonlinear control system design, an interactive computational tool is presented for fuzzy modeling and control. Practical aspects and a study of the digital implementation of fuzzy controllers are discussed using a Hardware-in-the-Loop (HIL) simulation with a Field Programmable Gate Array (FPGA) development board

Relaxed LMI conditions for control of nonlinear Takagi-Sugeno models

Los problemas de optimización de desigualdades matriciales lineales en control borroso se han convertido en la herramienta más utilizada en dicha área desde los años 90. Muchos sistemas no lineales pueden ser modelados como sistemas borrosos de modo que el control borroso puede considerarse como una técnica de control no lineal. Aunque se han obtenido muchos y buenos resultados, quedan algunas fuentes de conservadurismo cuando se comparan con otros enfoques de control no lineal. Esta tesis discute dichas cuestiones de conservadurismo y plantea nuevos enfoques para resolverlas. La principal ventaja de la formulación mediante desigualdades matriciales lineales es la posibilidad de asegurar estabilidad y prestaciones de un sistema no lineal modelado como un sistema borroso Takagi-Sugeno. Estos modelos están formados por un conjunto de modelos lineales eligiendo el sistema a aplicar mediante el uso de unas reglas borrosas. Estas reglas se traducen en funciones de interpolación o de pertenecía que nos indican el grado de validez de un modelo lineal respecto del resto. El mayor problema que presentan estas técnicas basadas en desigualdades matriciales lineales es que las funciones de pertenencia no están incluidas en las condiciones de estabilidad del sistema, lo que significa que se prueba la estabilidad y prestaciones para cualquier forma de interpolación entre los diferentes modelos lineales. Esto genera una fuente de conservadurismo que sería conveniente limitar. En la tesis doctoral se presentan varias metodologías capaces de trasladar la información de las funciones de pertenencia del sistema al problema basado en desigualdades matriciales lineales de estabilidad y prestaciones. Las dos principales aportaciones propuestas se basan, respectivamente, en introducir una serie de matrices de relajación que permitan incorporar esta información y en aprovechar la descripción de una amplia clase de sistemas borrosos en productos tensoriales de...Ariño Latorre, CV. (2008). Relaxed LMI conditions for control of nonlinear Takagi-Sugeno models [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8301Palanci