Output feedback controller design of Takagi–Sugeno fuzzy systems

This paper presents new systematic design methods of two types of output feedback controllers for Takagi–Sugeno (T–S) fuzzy systems, one of which is constructed with a fuzzy regulator and a fuzzy observer, while the other is an output direct feedback controller. In order to use the structural information in the rule base to decrease the conservatism of the stability analysis, the standard fuzzy partition (SFP) is employed to the premise variables of fuzzy systems. New stability conditions are obtained by relaxing the stability conditions derived in previous papers. The concept of parallel distributed compensation (PDC) is employed to design fuzzy regulators and fuzzy observers from the T–S fuzzy models. New stability analysis and design methods of output direct feedback controllers are also presented. The output feedback controllers design and simulation results for a nonlinear mass-spring-damper mechanical system show that these methods are effective.     

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.     

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.     

H 8 control for Takagi?Sugeno fuzzy systems

In this paper the design problem of output feedback H      

Stabilization for Takagi–Sugeno fuzzy systems based on partitioning the range of fuzzy weights

In this note, the state-feedback stabilization for continuous-time Takagi–Sugeno (T–S) fuzzy systems is addressed, where the fuzzy weighting functions are assumed to be differentiable and their ranges of variation are possibly bounded by some parameters. By utilizing the matrix elimination lemma and introducing a polyhedral partition to the range of the fuzzy weights, the quadratically parameterized condition is transformed to being piecewise linear in both the fuzzy weights and their derivatives. Then, a switching control based on the partition is considered, by utilizing the extreme points in each partition to address the constraints of the fuzzy weights and their derivatives. The simulation shows that finer subdivision in the partition leads to better stability and stabilization margins.     

Online identification of evolving Takagi–Sugeno–Kang fuzzy models for crane systems

This paper suggests new evolving Takagi–Sugeno–Kang (TSK) fuzzy models dedicated to crane systems. A set of evolving TSK fuzzy models with different numbers of inputs are derived by the novel relatively simple and transparent implementation of an online identification algorithm. An input selection algorithm to guide modeling is proposed on the basis of ranking the inputs according to their important factors after the first step of the online identification algorithm. The online identification algorithm offers rule bases and parameters which continuously evolve by adding new rules with more summarization power and by modifying existing rules and parameters. The potentials of new data points are used with this regard. The algorithm is applied in the framework of the pendulum–crane system laboratory equipment. The evolving TSK fuzzy models are tested against the experimental data and a comparison with other TSK fuzzy models and modeling approaches is carried out. The comparison points out that the proposed evolving TSK fuzzy models are simple and consistent with both training data and testing data and that these models outperform other TSK fuzzy models.     

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.     

Local and global optimization for Takagi–Sugeno fuzzy system by memetic genetic programming

This work presents a method to incorporate standard neuro-fuzzy learning for Takagi–Sugeno fuzzy systems that evolve under a grammar driven genetic programming (GP) framework. This is made possible by introducing heteroglossia in the functional GP nodes, enabling them to switch behavior according to the selected learning stage. A context-free grammar supports the expression of arbitrarily sized and composed fuzzy systems and guides the evolution. Recursive least squares and backpropagation gradient descent algorithms are used as local search methods. A second generation memetic approach combines the genetic programming with the local search procedures. Based on our experimental results, a discussion is included regarding the competitiveness of the proposed methodology and its properties. The contributions of the paper are: (i) introduction of an approach which enables the application of local search learning for intelligent systems evolved by genetic programming, (ii) presentation of a model for memetic learning of Takagi–Sugeno fuzzy systems, (iii) experimental results evaluating model variants and comparison with state-of-the-art models in benchmarking and real-world problems, (iv) application of the proposed model in control.     

Correction to: Sparse regressions and particle swarm optimization in training high-order Takagi–Sugeno fuzzy systems

Neural Computing and Applications - Unfortunately, the equation 39 has been published incorrectly in the online publication of the article.     

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.     

Optimal control for stochastic linear quadratic singular Takagi–Sugeno fuzzy delay system using genetic programming

In this paper, optimal control for stochastic linear singular Takagi–Sugeno (T–S) fuzzy delay system with quadratic performance is obtained using genetic programming (GP). To obtain the optimal control, the solution of matrix Riccati differential equation (MRDE) is computed by solving differential algebraic equation (DAE) using a novel and nontraditional GP approach. The GP solution is equivalent or very close to the exact solution of the problem. Accuracy of the GP solution to the problem is qualitatively better. The solution of this novel method is compared with the traditional Runge Kutta (RK) method. An illustrative numerical example is presented for the proposed method.     

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.     

Finite-time mixed H∞ and passive filtering for Takagi–Sugeno fuzzy nonhomogeneous Markovian jump systems

This paper is concerned with the finite-time mixed H_∞ and passivity performance analysis and filter design for a class of uncertain nonlinear discrete-time Markovian jump systems (MJSs) described by Takagi–Sugeno fuzzy model with nonhomogeneous jump processes. In this paper, the proposed MJSs fuzzy model is formulated with norm-bounded parameter uncertainties and time-varying jump transition probability matrices. In particular, the time-varying transition probability matrices are expressed in respect of a polytope. By constructing a suitable Lyapunov functional, a new set of sufficient conditions is derived in the form of linear matrix inequalities (LMIs) to ensure that the filtering error system is robustly stochastically finite-time bounded and a prescribed mixed H_∞ and passive performance index is achieved. Moreover, the robust mixed H_∞ and passivity filter design gain matrices can be computed from the obtained LMIs. Furthermore, the developed results unify H_∞ and passive filtering problems in a single framework. Finally, two numerical examples including an application-oriented example are provided to demonstrate the effectiveness of the proposed filter design technique.     

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.     

Evolving Takagi–Sugeno fuzzy model based on switching to neighboring models

In this paper, we propose a new online identification approach for evolving Takagi–Sugeno (TS) fuzzy models. Here, for a TS model, a certain number of models as neighboring models are defined and then the TS model switches to one of them at each stage of evolving. We define neighboring models for an in-progress (current) TS model as its fairly evolved versions, which are different with it just in two fuzzy rules. To generate neighboring models for the current model, we apply specially designed split and merge operations. By each split operation, a fuzzy rule is replaced with two rules; while by each merge operation, two fuzzy rules combine to one rule. Among neighboring models, the one with the minimum sum of squared errors – on certain time intervals – replaces the current model.To reduce the computational load of the proposed evolving TS model, straightforward relations between outputs of neighboring models and that of current model are established. Also, to reduce the number of rules, we define and use first-order TS fuzzy models whose generated local linear models can be localized in flexible fuzzy subspaces. To demonstrate the improved performance of the proposed identification approach, the efficiency of the evolving TS model is studied in prediction of monthly sunspot number and forecast of daily electrical power consumption. The prediction and modeling results are compared with that of some important existing evolving fuzzy systems.     

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.     

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.     

Observer-based H∞ fuzzy control for discrete-time Takagi–Sugeno fuzzy mixed delay systems with random packet losses and multiplicative noises

This paper investigates the observer-based H_∞ fuzzy control problem for a class of discrete-time fuzzy mixed delay systems with random communication packet losses and multiplicative noises, where the mixed delays comprise both discrete time-varying and distributed delays. The random packet losses are described by a Bernoulli distributed white sequence that obeys a conditional probability distribution, and the multiplicative disturbances are in the form of a scalar Gaussian white noise with unit variance. In the presence of mixed delays, random packet losses and multiplicative noises, sufficient conditions for the existence of an observer-based fuzzy feedback controller are derived, such that the closed-loop control system is asymptotically mean-square stable and preserves a guaranteed H_∞ performance. Then a linear matrix inequality approach for designing such an observer-based H_∞ fuzzy controller is presented. Finally, a numerical example is provided to illustrate the effectiveness of the developed theoretical results.