Performance Enhancement for T–S Fuzzy Control Using Neural Networks

A new control scheme is proposed to improve the system performance for Takagi–Sugeno (T–S) fuzzy system using control grade functions tuned by neural networks. First, systematic modeling method is introduced to construct the exact T–S fuzzy model for a nonlinear control system. For the T–S fuzzy model, the system uncertainty affects only the membership functions. To cope with this problem, the grade functions, resulting from the membership functions of the control rules, are tuned by a back-propagation network. On the other hand, the feedback gains of the control rules are determined by solving a set of linear matrix inequalities (LMIs) which satisfy sufficient conditions of the closed-loop stability. As a result, both stability guarantee and better performance are concluded. The scheme is applied to a ball-and-beam system example verified by numerical simulations.     

Stability Analysis and Performance Design for Fuzzy-Model-Based Control System Under Imperfect Premise Matching

This paper investigates the stability analysis and performance design of nonlinear systems. To facilitate the stability analysis, the Takagi–Sugeno (T–S) fuzzy model is employed to represent the nonlinear plant. Under the imperfect premise matching in which T–S fuzzy model and fuzzy controller do not share the same membership functions, a fuzzy controller with enhanced design flexibility and robustness property is proposed to control the nonlinear plant. However, the nice characteristic given by the perfect premise matching, leading to conservative stability conditions, vanishes. In this paper, under the imperfect premise matching, information of membership functions of the fuzzy model and controller are considered in stability analysis. With the introduction of slack matrices, relaxed linear matrix inequality (LMI)-based stability conditions are derived using Lyapunov-based approach. Furthermore, LMI-based performance conditions are provided to guarantee system performance. Simulation examples are given to illustrate the effectiveness of the proposed approach.      

Robust fuzzy control for uncertain discrete-time nonlinear Markovian jump systems without mode observations

This paper studies the robust fuzzy control problem of uncertain discrete-time nonlinear Markovian jump systems without mode observations. The Takagi and Sugeno (T-S) fuzzy model is employed to represent a discrete-time nonlinear system with norm-bounded parameter uncertainties and Markovian jump parameters. As a result, an uncertain Markovian jump fuzzy system (MJFS) is obtained. A stochastic fuzzy Lyapunov function (FLF) is employed to analyze the robust stability of the uncertain MJFS, which not only is dependent on the operation modes of the system, but also directly includes the membership functions. Then, based on this stochastic FLF and a non-parallel distributed compensation (non-PDC) scheme, a mode-independent state-feedback control design is developed to guarantee that the closed-loop MJFS is stochastically stable for all admissible parameter uncertainties. The proposed sufficient conditions for the robust stability and mode-independent robust stabilization are formulated as a set of coupled linear matrix inequalities (LMIs), which can be solved efficiently by using existing LMI optimization techniques. Finally, it is also demonstrated, via a simulation example, that the proposed design method is effective.     

Reliable$rm H_infty $Fuzzy Control for Continuous-Time Nonlinear Systems With Actuator Failures

This paper is concerned with the design of reliable$ H_infty $fuzzy controllers for continuous-time nonlinear systems with actuator failures. The Takagi and Sugeno fuzzy model is employed to represent a nonlinear system. The objective is to find a stabilizing state-feedback fuzzy controller such that the nominal$ H_infty $performance is optimized while satisfying a prescribed$ H_infty $performance constraint in the actuator failure cases. Based on the linear matrix inequality (LMI) techniques, two efficient methods for the design of a suboptimal reliable$ H_infty$fuzzy controller are proposed. Different Lyapunov functions are used during the design for the nominal and actuator failure cases, which lead to a less conservative controller design. In the first method, a single Lyapunov function is used for the actuator failure cases. The second method adopts a parameter-dependent Lyapunov function for the actuator failure cases, which further reduces the conservatism of the design. Finally, numerical simulations on the chaotic Rossler system are given to illustrate the effectiveness of the proposed design methods.     

A calibration approach based on Takagi–Sugeno fuzzy inference system for digital electronic compasses

Recently, the development of industrial processes brought on the outbreak of technologically complex systems. This development generated the necessity of research relative to the mathematical techniques that have the capacity to deal with project complexities and validation. Fuzzy models have been receiving particular attention in the area of nonlinear systems identification and analysis due to it is capacity to approximate nonlinear behavior and deal with uncertainty. A fuzzy rule-based model suitable for the approximation of many systems and functions is the Takagi–Sugeno (TS) fuzzy model. TS fuzzy models are nonlinear systems described by a set of if then rules which gives local linear representations of an underlying system. Such models can approximate a wide class of nonlinear systems. In this paper a performance analysis of a system based on TS fuzzy inference system for the calibration of electronic compass devices is considered. The contribution of the evaluated TS fuzzy inference system is to reduce the error obtained in data acquisition from a digital electronic compass. For the reliable operation of the TS fuzzy inference system, adequate error measurements must be taken. The error noise must be filtered before the application of the TS fuzzy inference system. The proposed method demonstrated an effectiveness of 57% at reducing the total error based on considered tests.     

Control and synchronization of chaotic systems using a novel indirect model reference fuzzy controller

This paper presents a robust indirect model reference fuzzy control scheme for control and synchronization of chaotic nonlinear systems subject to uncertainties and external disturbances. The chaotic system with disturbance is modeled as a Takagi–Sugeno fuzzy system. Using a Lyapunov function, stable adaptation laws for the estimation of the parameters of the Takagi–Sugeno fuzzy model are derived as well as what the control signal should be to compensate for the uncertainties. The synchronization of chaotic systems is also considered in the paper. It is shown that by the use of an appropriate reference signal, it is possible to make the reference model follow the master chaotic system. Then, using the proposed model reference fuzzy controller, it is possible to force the slave to act as the reference system. In this way, the chaotic master and the slave systems are synchronized. It is shown that not only can the initial values of the master and the slave be different, but also there can be parametric differences between them. The proposed control scheme is simulated on the control and the synchronization of Duffing oscillators and Genesio–Tesi systems.     

Identification of nonlinear systems by Takagi–Sugeno fuzzy logic grey box modeling for real-time control

Identification of nonlinear systems by fuzzy models has been successfully applied in many applications. Fuzzy models are capable of approximating any real continuous function to a chosen accuracy. An algorithm for real-time identification of nonlinear systems using Takagi–Sugeno's fuzzy models is presented in this paper. A Takagi–Sugeno fuzzy system is trained incrementally each time step and is used to predict one-step ahead system output. Ability of the proposed identifier to capture the nonlinear behavior of a synchronous machine is illustrated. Effectiveness of the proposed identification technique is demonstrated by simulation and experimental studies on a power system.     

Parallel Distributed Fuzzy Sliding Mode Control for Nonlinear Mismatched Uncertain Systems

A new design approach of a parallel distributed fuzzy sliding mode controller for nonlinear systems with mismatched time varying uncertainties is presented in this paper. The nonlinear system is approximated by the Takagi–Sugeno fuzzy linear model. The approximation error between the nonlinear system and the fuzzy linear model is considered as one part of the uncertainty in the uncertain nonlinear system. The time varying uncertainties are assumed to have the format which enables the design of the coefficient matrix of the sliding function to satisfy a sliding coefficient matching condition. With the sliding coefficient matching condition satisfied, a parallel distributed fuzzy sliding mode controller (PDFSC) is designed. The stability and the sliding mode of the fuzzy sliding control system are guaranteed. Also, the nonlinear system is shown to be invariant on the sliding surface. Moreover, the chattering around the sliding surface in the sliding mode control can be reduced by the proposed design approach. Simulation results are included to illustrate the effectiveness of the proposed fuzzy sliding mode controller. This work is partly supported by the the R.O.C. National Science Council through Grant NSC93-2213-E-197-004.     

Reliable LQ fuzzy control for nonlinear discrete-time systems via LMIs.

This paper studies reliable linear quadratic (LQ) fuzzy regulator problem for nonlinear discrete-time systems with actuator faults. The Takagi and Sugeno fuzzy model is employed to represent a nonlinear system. A sufficient condition expressed in linear matrix inequality (LMI) terms for the existence of reliable guaranteed cost (GC) fuzzy controllers is obtained. The fuzzy controller directly obtained from the LMI solutions can guarantee the stability of the closed-loop overall fuzzy system, while provide a guaranteed cost on the quadratic cost function of the system in the normal and actuator fault cases. Furthermore, an optimal reliable GC fuzzy controller in the sense of minimizing a bound on the worst or nominal case guaranteed cost is also given by means of an LMI optimization procedure. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.     

A novel criterion for nonlinear time-delay systems using LMI fuzzy Lyapunov method

This study presents a kind of fuzzy robustness design for nonlinear time-delay systems based on the fuzzy Lyapunov method, which is defined in terms of fuzzy blending quadratic Lyapunov functions. The basic idea of the proposed approach is to construct a fuzzy controller for nonlinear dynamic systems with disturbances in which the delay-independent robust stability criterion is derived in terms of the fuzzy Lyapunov method. Based on the robustness design and parallel distributed compensation (PDC) scheme, the problems of modeling errors between nonlinear dynamic systems and Takagi–Sugeno (T–S) fuzzy models are solved. Furthermore, the presented delay-independent condition is transformed into linear matrix inequalities (LMIs) so that the fuzzy state feedback gain and common solutions are numerically feasible with swarm intelligence algorithms. The proposed method is illustrated on a nonlinear inverted pendulum system and the simulation results show that the robustness controller cannot only stabilize the nonlinear inverted pendulum system, but has the robustness against external disturbance.     

Non-monotonic robust H2 fuzzy observer-based control for discrete time nonlinear systems with parametric uncertainties

A non-monotonic Lyapunov function (NMLF) is deployed to design a robust H₂ fuzzy observer-based control problem for discrete-time nonlinear systems in the presence of parametric uncertainties. The uncertain nonlinear system is presented as a Takagi and Sugeno (T–S) fuzzy model with norm-bounded uncertainties. The states of the fuzzy system are estimated by a fuzzy observer and the control design is established based on a parallel distributed compensation scheme. In order to derive a sufficient condition to establish the global asymptotic stability of the proposed closed-loop fuzzy system, an NMLF is adopted and an upper bound on the quadratic cost function is provided. The existence of a robust H₂ fuzzy observer-based controller is expressed as a sufficient condition in the form of linear matrix inequalities (LMIs) and a sub-optimal fuzzy observer-based controller in the sense of cost bound minimization is obtained by utilising the aforementioned LMI optimisation techniques. Finally, the effectiveness of the proposed scheme is shown through an example.     

Robustness design of nonlinear dynamic systems via fuzzy linearcontrol

This study introduces a fuzzy linear control design method for nonlinear systems with optimal H^∞ robustness performance. First, the Takagi and Sugeno fuzzy linear model (1985) is employed to approximate a nonlinear system. Next, based on the fuzzy linear model, a fuzzy controller is developed to stabilize the nonlinear system, and at the same time the effect of external disturbance on control performance is attenuated to a minimum level. Thus based on the fuzzy linear model, H^∞ performance design can be achieved in nonlinear control systems. In the proposed fuzzy linear control method, the fuzzy linear model provides rough control to approximate the nonlinear control system, while the H^∞ scheme provides precise control to achieve the optimal robustness performance. Linear matrix inequality (LMI) techniques are employed to solve this robust fuzzy control problem. In the case that state variables are unavailable, a fuzzy observer-based H^∞ control is also proposed to achieve a robust optimization design for nonlinear systems. A simulation example is given to illustrate the performance of the proposed design method     

On Maximum Stability Margin Design of Nonlinear Uncertain Systems: Fuzzy Control Approach

This paper studies the maximum stability margin design for nonlinear uncertain systems using fuzzy control. First, the Takagi and Sugeno fuzzy model is employed to approximate a nonlinear uncertain system. Next, based on the fuzzy model, the maximum stability margin for a nonlinear uncertain system is studied to achieve as much tolerance of plant uncertainties as possible using a fuzzy control method. In the proposed fuzzy control method, the maximum stability margin design problem is parameterized in terms of a corresponding generalized eigenvalue problem (GEVP). For the case where state variables are unavailable, a fuzzy observer‐based control scheme is also proposed to deal with the maximum stability margin for nonlinear uncertain systems. Using a suboptimal approach, we characterize the maximum stability margin via fuzzy observer‐based control in terms of a linear matrix inequality problem (LMIP). The GEVP and LMIP can be solved very efficiently via convex optimization techniques. Simulation examples are given to illustrate the design procedure of the proposed method.     

Guaranteed Cost Control of Polynomial Fuzzy Systems via a Sum of Squares Approach

This paper presents the guaranteed cost control of polynomial fuzzy systems via a sum of squares (SOS) approach. First, we present a polynomial fuzzy model and controller that are more general representations of the well-known Takagi–Sugeno (T-S) fuzzy model and controller, respectively. Second, we derive a guaranteed cost control design condition based on polynomial Lyapunov functions. Hence, the design approach discussed in this paper is more general than the existing LMI approaches (to T-S fuzzy control system designs) based on quadratic Lyapunov functions. The design condition realizes a guaranteed cost control by minimizing the upper bound of a given performance function. In addition, the design condition in the proposed approach can be represented in terms of SOS and is numerically (partially symbolically) solved via the recent developed SOSTOOLS. To illustrate the validity of the design approach, two design examples are provided. The first example deals with a complicated nonlinear system. The second example presents micro helicopter control. Both the examples show that our approach provides more extensive design results for the existing LMI approach.      

三级倒立摆的加权变量模糊神经网络控制

为了提高三级倒立摆系统控制的响应速度和稳定性,在设计Mamdani型摸糊推理规则控制器控制倒立摆系统稳定的基础上,设计了一种更有效率的基于Sugeno型模糊推理规则的模糊神经网络控制器。该控制器使用BP神经网络和最小二乘法的混合算法进行参数训练,能够准确归纳输入输出量的模糊隶属度函数和模糊逻辑规则。通过与Mamdani型控制器的仿真对比,表明该Sugeno型模糊神经网络控制器对三级倒立摆系统的控制具有良好的稳定性和快速性,以及较高的控制精度。     

A nonlinear state‐feedback state‐feedforward tracking control strategy for a boiler‐turbine unit

A boiler‐turbine unit is a primary module for coal‐fired power plants, and an effective automatic control system is needed for the boiler‐turbine unit to track the load changes with the drum water level kept within an acceptable range. The aim of this paper is to develop a nonlinear tracking controller for the Bell‐Åström boiler‐turbine unit. A Takagi‐Sugeno fuzzy control system is introduced for the nonlinear modeling of the Bell‐Åström boiler‐turbine unit. Based on the Takagi‐Sugeno fuzzy models, a nonlinear tracking controller is developed, and the proposed control law is comprised of a state‐feedforward term and a state‐feedback term. The stability of the closed‐loop control system is analyzed on the basis of Lyapunov stability theory via the linear matrix inequality approach and Schur complement. Moreover, model uncertainties are also considered, and it is proved that with the proposed control law the tracking error converges to zero. To assess the performance of the proposed nonlinear state‐feedback state‐feedforward control strategy, a nonlinear model predictive control strategy and a linear strategy are presented as comparisons. The effectiveness and the advantages of the proposed nonlinear state‐feedback state‐feedforward control strategy are demonstrated by simulations.     

Supervision of nonlinear adaptive controllers based on fuzzy models

A novel approach for the supervision of fuzzy model on-line adaptation is proposed. A nonlinear predictive controller is designed based on a Takagi–Sugeno fuzzy model. By adapting the fuzzy model on-line, high control performance can be achieved even with time-variant process behaviour and changing unmodelled disturbances. A local weighted recursive least-squares algorithm exploits the local linearity of Takagi–Sugeno fuzzy models. In order to cope with problems resulting from insufficient excitation, a supervisory level is introduced. It comprises a variable forgetting factor and an additional adaptation model which makes the on-line adaptation robust and reliable. The effectiveness and real-world applicability of the proposed approach are demonstrated by application to temperature control of a heat exchanger.     

Modeling of an inverted pendulum based on fuzzy clustering techniques

The inverted pendulum is a highly nonlinear and open loop unstable system. To develop an accurate model of the inverted pendulum, different linear and nonlinear methods of identification will be used. However one of the problems encountered during modeling is the collection of experimental data from the inverted pendulum system. Since the output data from the unstable system does not show enough information or dynamics of the system. This can be overcome by designing a feedback controller, which stabilize the system before identification can takes place. Recently Takagi–Sugeno (T–S) fuzzy modeling based on clustering techniques have shown great progress in identification of nonlinear systems. Hence in this paper, Takagi–Sugeno (T–S) model is proposed for an inverted pendulum based on fuzzy c-means, Gustafson–Kessel (G–K) and Gath–Geva clustering techniques. Simulation results show that Gustafson–Kessel (G–K) clustering technique produces satisfactory performance.     

Robust adaptive fuzzy VSS control for a class of uncertain nonlinear systems using small gain design

In this paper, a novel robust adaptive fuzzy variable structure control (RAFVSC) scheme is proposed for a class of uncertain nonlinear systems. The uncertain nonlinear system and gain functions originating from modeling errors and external disturbances are all unstructured (or non-repeatable), state-dependent and completely unknown. The Takagi–Sugeno type fuzzy logic systems are used to approximate uncertain functions in the systems and the RAFVSC is designed by use of the input-to-state stability (ISS) approach and small gain theorem. In the algorithm, there are three advantages which are that the asymptotic stability of adaptive control in the presence of unstructured uncertainties can be guaranteed, the possible controller singularity problem in some of existing adaptive control schemes using feedback linearization techniques can be removed and the adaptive mechanism with minimal learning parameterizations can be achieved. The performance and effectiveness of the proposed methods are discussed and illustrated with two simulation examples.     

Mode-independent robust stabilization for uncertain Markovian jump nonlinear systems via fuzzy control.

This paper is concerned with the robust-stabilization problem of uncertain Markovian jump nonlinear systems (MJNSs) without mode observations via a fuzzy-control approach. The Takagi and Sugeno (T-S) fuzzy model is employed to represent a nonlinear system with norm-bounded parameter uncertainties and Markovian jump parameters. The aim is to design a mode-independent fuzzy controller such that the closed-loop Markovian jump fuzzy system (MJFS) is robustly stochastically stable. Based on a stochastic Lyapunov function, a robust-stabilization condition using a mode-independent fuzzy controller is derived for the uncertain MJFS in terms of linear matrix inequalities (LMIs). A new improved LMI formulation is used to alleviate the interrelation between the stochastic Lyapunov matrix and the system matrices containing controller variables in the derivation process. Finally, a simulation example is presented to illustrate the effectiveness of the proposed design method.