Fuzzy control and filter design for uncertain fuzzy systems
Most real physical systems are nonlinear in nature. Controlling and filtering nonlinear systems are still open problems due to their complexity natures. These problems become more complex when the system's parameters are uncertain. In recent years, a large number of practical control problems have involved designing a controller/filter that minimizes the worst-case ratio of output energy (filter error energy) to disturbance energy which is known as an \(H^\infty\) control (filter) problem. The \(H^\infty\) control or filter problem is able to address the issue of system parameter uncertainty, and also be applied to the typical problem of disturbance input control. The focus of this book is to establish novel methodologies for designing robust \(H^\infty\) fuzzy controllers and robust \(H^\infty\) fuzzy filters for a class of UNSs (Uncertain Nonlinear Systems), UNMJSs (Uncertain Nonlinear Markovian Jump Systems), UNSPSs (Uncertain Nonlinear Singularly Perturbed Systems) and UNSPS-MJs (Uncertain Nonlinear Singularly Perturbed Systems with Markovian Jump) which are described by a TS (Takagi-Sugeno) fuzzy system with parametric uncertainties and with/without MJs (Markovian Jump Systems). To investigate the design problems, the authors first describe a class of UNSs, UNMJSs, UNSPSs and UNSPS-MJs by a TS fuzzy system with parametric uncertainties and with/without MJs. Then, based on an LMI (Linear Matrix Inequalities) approach, the authors develop a technique for designing robust \(H^\infty\) fuzzy controllers and robust \(H^\infty\) fuzzy filters such that a given prescribed performance index is guaranteed. The book has been divided into two parts: In Part I, the new design methodology on a robust \(H^\infty\) fuzzy controller and a robust \(H^\infty\) fuzzy filter for a class of UFSs (Uncertain Fuzzy Systems) and UFMJSs (Uncertain Fuzzy Markovian Jump Systems) has been developed. This new design approach allows one to achieve designing the robust \(H^\infty\) fuzzy controller and the robust \(H^\infty\) fuzzy filter for a class of UNSs and UNMJSs in a unified framework, which is based on the TS fuzzy model and LMIs approach. The proposed design result satisfies all admissible noises, disturbances and uncertainties. In Part II, the design methodology on a robust \(H^\infty\) fuzzy controller and a robust \(H^\infty\) fuzzy filter for a class of UFSPSs (Uncertain Fuzzy Singularly Perturbed Systems) and UFSPS-MJs (Uncertain Fuzzy Singularly Perturbed Systems with Markovian Jump) has been presented. The proposed design approach in this part for a class of UFSPSs and UFSPS-MJs does not involve the separation of states into slow and fast ones and it can be applied not only to standard, but also to nonstandard nonlinear singularly perturbed systems. Furthermore, the proposed approach shows that the design result satisfies all admissible noises, disturbances and uncertainties. Finally, to demonstrate the effectiveness and advantages of the proposed design methodologies in this thesis, applications to UNS, UNMJS, UNSPS and UNSPS-MJ (i.e., a motor, a tunnel diode circuit and an economic model) are given as examples in each chapter. The simulation results show that the proposed design methodologies can achieve the prescribed performance index.
fuzzy control design, \(H^\infty\) fuzzy filter design, fuzzy Markovian jump systems, fuzzy singularly perturbed systems
scientific article; zbMATH DE number 5076748