Zonotopic fault detection observer design for Takagi–Sugeno fuzzy systems

This paper considers zonotopic fault detection observer design in the finite-frequency domain for discrete-time Takagi–Sugeno fuzzy systems with unknown but bounded disturbances and measurement noise. We present a novel fault detection observer structure, which is more general than the commonly used Luenberger form. To make the generated residual sensitive to faults and robust against disturbances, we develop a finite-frequency fault detection observer based on generalised Kalman–Yakubovich–Popov lemma and P-radius criterion. The design conditions are expressed in terms of linear matrix inequalities. The major merit of the proposed method is that residual evaluation can be easily implemented via zonotopic approach. Numerical examples are conducted to demonstrate the proposed method.     

Output feedback controller design for uncertain piecewise linear systems

This paper proposes output feedback controller design methods for uncertain piecewise linear systems based on piecewise quadratic Lyapunov function. The α-stability of closed-loop systems is also considered. It is shown that the output feedback controller design procedure of uncertain piecewise linear systems with α-stability constraint can be cast as solving a set of bilinear matrix inequalities （BMIs）. The BMIs problem in this paper can be solved iteratively as a set of two convex optimization problems involving linear matrix inequalities （LMIs） which can be solved numerically efficiently. A numerical example shows the effectiveness of the proposed methods.     

State feedback control of interval type-2 Takagi–Sugeno fuzzy systems via interval type-2 regional switching fuzzy controllers

The interval type-2 Takagi–Sugeno fuzzy systems have been proposed to handle nonlinear systems subject to parameter uncertainties. In this paper, a new type of state feedback controller, namely, interval type-2 regional switching fuzzy controller, is proposed to conceive less-conservative stabilisation conditions, which is switched by basing on the values of system states. To further reduce the conservativeness in the stability analysis, the information of lower and upper membership functions is also considered. Stability conditions for the interval type-2 fuzzy closed-loop systems are presented in the form of linear matrix inequalities (LMIs). Simulation examples are provided to illustrate the effectiveness of the proposed method.     

Absolute stability analysis for a class of Takagi–Sugeno fuzzy control systems

This article presents absolute stability conditions for a particular class of Takagi–Sugeno fuzzy control systems. Initially, a Takagi–Sugeno fuzzy control system is transformed into a multivariable Lur’e type system. A simple algorithm for checking the absolute stability of this system is then proposed. Since the key of the proposed algorithm is to solve algebraic Riccati equations, software packages such as MATLAB provides a simple means to check the conditions. The proposed approach does not limit the methods of fuzzification and defuzzification. This article presents several analytical examples to verify the simplicity and efficiency of the proposed approach.     

Fault reconstruction for Takagi–Sugeno fuzzy systems via learning observers

This paper addresses the problem of observer-based fault reconstruction for Takagi–Sugeno fuzzy systems. Two types of fuzzy learning observers are constructed to achieve simultaneous reconstruction of system states and actuator faults. Stability and convergence of the proposed observers are proved using Lyapunov stability theory, and necessary conditions for the existence of the observers are further discussed. The design of fuzzy learning observers can be formulated in terms of a series of linear matrix inequalities that can be conveniently solved using convex optimisation technique. A single-link flexible manipulator is employed to verify the effectiveness of the proposed fault-reconstructing approaches.     

Non-fragile guaranteed cost control for Takagi–Sugeno fuzzy hyperbolic systems

This paper concerns the problems of non-fragile guaranteed cost control (GCC) for nonlinear systems with or without parameter uncertainties. The Takagi–Sugeno (T–S) fuzzy hyperbolic model is employed to represent the nonlinear system. The non-fragile controller is designed by parallel distributed compensation (PDC) method, and some sufficient conditions are formulated via linear matrix inequalities (LMIs) such that the system is asymptotically stable and the cost function satisfies an upper bound in the presence of the additive controller perturbations. The above approach is also extended to the non-fragile GCC of T–S fuzzy hyperbolic system with parameter uncertainties, and the robust non-fragile GCC scheme is obtained. The main advantage of the non-fragile GCC based on the T–S fuzzy hyperbolic model is that it can achieve small control amplitude via ‘soft’ constraint approach. Finally, a numerical example and the Van de Vusse example are given to illustrate the effectiveness and feasibility of the proposed approach.     

Non-fragile H∞ dynamic output feedback control for uncertain Takagi–Sugeno fuzzy systems with time-varying delay

This paper mainly focuses on the problem of non-fragile H_∞ dynamic output feedback control for a class of uncertain Takagi–Sugeno fuzzy systems with time-varying state delay. Based on a new type of Lyapunov–Krasovskii functional without ignoring any subtle integral terms in the derivatives, a less conservative dynamic output feedback controller with additive gain variations is designed, which guarantees that the closed-loop fuzzy system is asymptotically stable and satisfies a prescribed H_∞-performance level. Furthermore, the obtained parameter-dependent conditions are given in terms of solution to a set of linear matrix inequalities, which improve some existing relevant results. Finally, numerical examples are given to illustrate the effectiveness and merits of the proposed method.     

On reducing computational overhead in multi-objective genetic Takagi–Sugeno fuzzy systems

The use of multi-objective evolutionary algorithms (MOEAs) to generate a set of fuzzy rule-based systems (FRBSs) with different trade-offs between complexity and accuracy has gained more and more interest in the scientific community. The evolutionary process requires, however, a large number of FRBS generations and evaluations. When we deal with high dimensional datasets, these tasks can be very time-consuming, especially when we generate Takagi–Sugeno FRBSs, thus making a satisfactory exploration of the search space very awkward. In this paper, we first analyze the time complexity for both the generation and the evaluation of Takagi–Sugeno FRBSs. Then we introduce a simple but effective technique for speeding up the identification of the rule consequent parameters, one of the most time-consuming phases in Takagi–Sugeno FRBS generation. Finally, we highlight how the application of this technique produces as a side-effect a decoupling of the rules. This decoupling allows us to avoid re-computing consequent parameters of rules which are not directly modified during the evolutionary process, thus saving a considerable amount of time.In the experimental part we first test the correctness of the predicted asymptotical time complexity. Then we show the benefits in terms of computing time saving and improved search space exploration through an example of multi-objective genetic learning of Takagi–Sugeno FRBSs in the regression domain.     

A fuzzy Lyapunov function approach to estimating the domain of attraction for continuous-time Takagi–Sugeno fuzzy systems

This paper deals with stability analysis and control design problems for continuous-time Takagi–Sugeno (T–S) fuzzy systems. The first aim is to present less conservative linear matrix inequality (LMI) conditions to design controllers and assess the stability. The second relevant contribution is to present a new strategy to find an inner estimate of the domain of attraction (DA) via LMIs. The results are based on the fuzzy Lyapunov functions (FLFs) and non-parallel distributed compensation (non-PDC) approaches. Finally, examples illustrate the effectiveness and merits of the proposed methods.     

AQM router design for TCP network via input constrained fuzzy control of time-delay affine Takagi–Sugeno fuzzy models

In this article, Takagi–Sugeno (T–S) fuzzy control theory is proposed as a key tool to design an effective active queue management (AQM) router for the transmission control protocol (TCP) networks. The probability control of packet marking in the TCP networks is characterised by an input constrained control problem in this article. By modelling the TCP network into a time-delay affine T–S fuzzy model, an input constrained fuzzy control methodology is developed in this article to serve the AQM router design. The proposed fuzzy control approach, which is developed based on the parallel distributed compensation technique, can provide smaller probability of dropping packets than previous AQM design schemes. Lastly, a numerical simulation is provided to illustrate the usefulness and effectiveness of the proposed design approach.     

Relaxed stability condition and state feedback H ∞ controller design for T-S fuzzy systems

In this paper, a fuzzy Lyapunov approach is presented for stability analysis and state feedback H _∞ controller design for T-S fuzzy systems. A new stability condition is obtained by relaxing the ones derived in previous papers. Then, a set of LMI-based sufficient conditions which can guarantee the existence of state feedback H _∞ controller for T-S fuzzy systems is proposed. In comparison with the existing literature, the proposed approach not only provides more relaxed stability conditions but also ensures better H _∞ performance. The effectiveness of the proposed approach is shown through two numerical examples. Recommended by Editor Young-Hoon Joo. Xiao-Heng Chang received the B.E. and M.S. degrees from Liaoning Technical University, China, in 1998 and 2004, respectively, and the Ph.D. degree from Northeastern University, China, in 2007. He is currently a Lecturer in the School of Information Science and Engineering, Bohai University, China. His research interests include fuzzy control and robust control as well as their applications. Guang-Hong Yang received the B.S. and M.S. degrees in Northeast University of Technology, China, in 1983 and 1986, respectively, and the Ph.D. degree in Control Engineering from Northeastern University, China (formerly, Northeast University of Technology), in 1994. He was a Lecturer/Associate Professor with Northeastern University from 1986 to 1995. He joined the Nanyang Technological University in 1996 as a Postdoctoral Fellow. From 2001 to 2005, he was a Research Scientist/Senior Research Scientist with the National University of Singapore. He is currently a Professor at the College of Information Science and Engineering, Northeastern University. His current research interests include fault-tolerant control, fault detection and isolation, nonfragile control systems design, and robust control. Dr. Yang is an Associate Editor for the International Journal of Control, Automation, and Systems (IJCAS), and an Associate Editor of the Conference Editorial Board of the IEEE Control Systems Society.     

Guaranteed cost control analysis and iterative design for constrained Takagi–Sugeno systems

This paper presents a novel control design technique in order to obtain a guaranteed cost fuzzy controller subject to constraints on the input channel. This guaranteed cost control law is obtained via multi-parametric quadratic programming. The result is a piecewise fuzzy control law where the state partition is defined by fuzzy inequalities. The parameters of the Lyapunov function can be obtained previously using Linear Matrix Inequalities optimization.     

Robust H ∞ reliable control of time delay nonlinear systems via Takagi–Sugeno fuzzy models

This article is focused on reliable fuzzy H _∞ controller design for a class of Takagi–Sugeno (T–S) fuzzy systems with state delay, actuator failures, disturbance input and norm bounded uncertainties. In the design, the H _∞ performance of the closed-loop system is optimised during normal operation (without failures) while the system satisfies a prescribed H _∞ performance level in the case of actuator failures. Two methods are presented in this study. In the first method, delay-dependent conditions are derived based on a single Lyapunov–Krasovskii function. This method improves delay-independent results existing in the literature. Next, to further reduce the conservatism, we use a parameter-dependent Lyapunov–Krasovskii function. The new sufficient conditions for the existence of the suboptimal robust reliable controller are shown in terms of linear matrix inequalities (LMIs), which can be solved by using LMI optimisation techniques. A simulation example shows the effectiveness of the proposed methods.     

Structure and stability analysis of a Takagi–Sugeno fuzzy PI controller with application to tissue hyperthermia therapy

 In this paper, we first reveal the analytical structure of a simple Takagi–Sugeno (TS) fuzzy PI controller relative to the linear PI controller. The fuzzy controller consists of two linear input fuzzy sets, four TS fuzzy rules with linear consequent, Zadeh fuzzy logic AND and the centroid defuzzifier. We prove that the fuzzy controller is actually a nonlinear PI controller with the gains changing with process output. Utilizing the well-known small Gain Theorem in control theory, we then derive sufficient conditions for global stability of the fuzzy control systems involving the TS fuzzy PI controller. Finally, as an application demonstration, we apply the fuzzy PI controller to control issue temperature, in computer simulation, during hyperthermia therapy. The relationship between heat energy and tissue temperature is represented by a linear time-varying model with a time delay. The sufficient conditions for global stability are used to design a stable fuzzy control system. Our simulation results show that the fuzzy PI control system achieves satisfactory temperature control performance. The control system is robust and stable even when the model parameters are changed suddenly and significantly.     

Optimal control of Takagi–Sugeno fuzzy-model-based systems representing dynamic ship positioning systems

Orthogonal function approach (OFA) and the hybrid Taguchi-genetic algorithm (HTGA) are used to solve quadratic finite-horizon optimal controller design problems in both a fuzzy parallel distributed compensation (PDC) controller and a non-PDC controller (linear state feedback controller) for Takagi–Sugeno (TS) fuzzy-model-based control systems for dynamic ship positioning systems (TS-DSPS). Based on the OFA, an algorithm requiring only algebraic computation is used to solve dynamic equations for TS-fuzzy-model-based feedback and is then integrated with HTGA to design quadratic finite-horizon optimal controllers for TS-DSPS under the criterion of minimizing a quadratic finite-horizon integral performance index, which is also converted to algebraic form by the OFA. Integration of OFA and HTGA in the proposed approach enables use of simple algebraic computation and is well adapted to the computer implementation. Therefore, it facilitates design tasks of quadratic finite-horizon optimal controllers for the TS-DSPS. The applicability of the proposed approach is demonstrated in the example of a moored tanker designed using quadratic finite-horizon optimal controllers.     

Application of evolving Takagi–Sugeno fuzzy model to nonlinear system identification

In this paper, a new encoding scheme is presented for learning the Takagi–Sugeno (T–S) fuzzy model from data by genetic algorithms (GAs). In the proposed encoding scheme, the rule structure (selection of rules and number of rules), the input structure (selection of inputs and number of inputs), and the antecedent membership function (MF) parameters of the T–S fuzzy model are all represented in one chromosome and evolved together such that the optimisation of rule structure, input structure, and MF parameters can be achieved simultaneously. The performance of the developed evolving T–S fuzzy model is first validated by studying the benchmark Box–Jenkins nonlinear system identification problem and nonlinear plant modelling problem, and comparing the obtained results with other existing results. Then, it is applied to approximate the forward and inverse dynamic behaviours of a magneto-rheological (MR) damper of which identification problem is significantly difficult due to its inherently hysteretic and highly nonlinear dynamics. It is shown by the validation applications that the developed evolving T–S fuzzy model can identify the nonlinear system satisfactorily with acceptable number of rules and appropriate inputs.