Stable nonlinear controller design for a Takagi-Sugeno fuzzy model

This paper proposes another adaptive control scheme for nonlinear systems using a Takagi-Sugeno fuzzy model. Takagi-Sugeno fuzzy models have been widely used to identify the structures and parameters of unknown or partially known plants, and to control nonlinear systems. This scheme shows a good approximation capability by the fuzzy blending of local dynamics. Since a Takagi-Sugeno fuzzy model is a nonlinear system in nature, and its parameters are not linearly parameterized, it is difficult to design an adaptive controller using conventional design methods for adaptive controllers which are derived from linearly parameterized systems. In this paper, the functional form of the local dynamics are assumed to be known, but the corresponding parameters are unknown. This additional information about system nonlinearity makes it possible to design an adaptive controller for a nonlinearly parameterized system. The control law is similar to that of a conventional adaptive control technique, while its parameter-update rule is based on the local search method. A parameter-update law is derived so that the time-derivative of the Lyapunov function is negative in the region of interest. Simulation results have shown that this adaptive controller is capable of a good performance. This work was presented in part at the Fifth International Symposium on Artificial Life and Robotics, Oita, Japan, January 26–28, 2000     

Adaptive Synchronization of Uncertain Chaotic Systems Based on T–S Fuzzy Model

This paper presents an adaptive approach for synchronization of Takagi-Sugeno (T-S) fuzzy chaotic systems. T-S fuzzy model can represent a general class of nonlinear system and we employ it for fuzzy modeling of the chaotic drive system. Since the output of the drive system is only available for synchronization, the response system is designed based on fuzzy adaptive observer for uncertain parameters and parameter mismatch cases. We analyze the stability of the overall fuzzy synchronization system by applying Lyapunov stability theory and derive stability conditions by solving linear matrix inequalities (LMIs) problem. The adaptive law is derived to estimate the uncertain parameters or parameter mismatch. Numerical examples are given to demonstrate the validity of the proposed fuzzy adaptive synchronization approach.     

Stable Adaptive Fuzzy Control with TSK Fuzzy Friction Estimation for Linear Drive Systems

This paper considers the control of a linear drive system with friction and disturbance compensation. A stable adaptive controller integrated with fuzzy model-based friction estimation and switching-based disturbance compensation is proposed via Lyapunov stability theory. A TSK fuzzy model with local linear friction models is suggested for real-time estimation of its consequent local parameters. The parameters update law is derived based on linear parameterization. In order to compensate for the effects resulting from estimation error and disturbance, a robust switching law is incorporated in the overall stable adaptive control system. Extensive computer simulation results show that the proposed stable adaptive fuzzy control system has very good performances, and is potential for precision positioning and trajectory tracking control of linear drive systems.     

Globally stable model reference adaptive control based on fuzzy description of the plant

A novel fuzzy adaptive control algorithm is presented that belongs to direct model reference adaptive techniques based on a fuzzy (Takagi-Sugeno) model of the plant. The global stability of the overall system is proven, namely all the signals in the system remain bounded while the tracking error and estimated parameters converge to some residual set that depends on the size of disturbance and high-order parasitic dynamics. The hallmarks of the approach are its simplicity and transparency. The proposed algorithm is a straightforward extension of classical model reference adaptive control (MRAC) with a robust adaptive law to nonlinear systems described by fuzzy models. The performance of the approach was tested on a simulated plant and compared with the performance of a PI controller and a classical MRAC.     

Direct fuzzy model‐reference adaptive control

Intelligent systems may be viewed as a framework for solving the problems of nonlinear system control. The intelligence of the system in the nonlinear or changing environment is used to recognize in which environment the system currently resides and to service it appropriately. This paper presents a general methodology of adaptive control based on multiple models in fuzzy form to deal with plants with unknown parameters which depend on known plant variables. We introduce a novel model‐reference fuzzy adaptive control system which is based on the fuzzy basis function expansion. The generality of the proposed algorithm is substantiated by the Stone‐Weierstrass theorem which indicates that any continuous function can be approximated by fuzzy basis function expansion. In the sense of adaptive control this implies the adaptive law with fuzzified adaptive parameters which are obtained using Lyapunov stability criterion. The combination of adaptive control theory based on models obtained by fuzzy basis function expansion results in fuzzy direct model‐reference adaptive control which provides higher adaptation ability than basic adaptive‐control systems. The proposed control algorithm is the extension of direct model‐reference fuzzy adaptive‐control to nonlinear plants. The direct fuzzy adaptive controller directly adjusts the parameter of the fuzzy controller to achieve approximate asymptotic tracking of the model‐reference input. The main advantage of the proposed approach is simplicity together with high performance, and it has been shown that the closed‐loop system using the direct fuzzy adaptive controller is globally stable and the tracking error converges to the residual set which depends on fuzzification properties. The proposed approach can be implemented on a wide range of industrial processes. In the paper the foundation of the proposed algorithm are given and some simulation examples are shown and discussed. © 2002 Wiley Periodicals, Inc.     

Fuzzy system as parameter estimator of nonlinear dynamic functions

In this paper we use adaptive fuzzy systems as intelligent identification systems for nonlinear time-varying plants. A new technique to design the fuzzy system that relies on the minimization of a loss function is presented. The design technique uses the centers of the fuzzy sets (labels) at the antecedent part of the rule base as the estimated parameters. This parametrization has the Linear In The Parameters (LITPs) characteristic that allows standard parameter estimation technique to be used to estimate the parameters of the fuzzy system. The combination of the fuzzy system and the estimation method then performs as a nonlinear estimator. If several fuzzy sets are defined for the input variables at the antecedent part, the fuzzy system ("fuzzy estimator") then behaves as a collection of nonlinear estimators where different rules' regions have different parameters. The proposed scheme is potentially capable of estimating the parameters of highly nonlinear plants. Simulation examples, which use plants with highly nonlinear gain, show the power of the proposed estimation scheme in comparison to estimation using the linear model.     

Fuzzy dynamic output feedback control with adaptive rotor imbalance compensation for magnetic bearing systems

This paper presents a dynamic output feedback control with adaptive rotor-imbalance compensation based on an analytical Takagi-Sugeno fuzzy model for complex nonlinear magnetic bearing systems with rotor eccentricity. The rotor mass-imbalance effect is considered with a linear in the parameter approximator. Through the robust analysis for disturbance rejection, the control law can be synthesized in terms of linear matrix inequalities. Based on the suggested fuzzy output feedback design, the controller may be much easier to implement than conventional nonlinear controllers. Simulation validations show that the proposed robust fuzzy control law can suppress the rotor imbalance-induced vibration and has excellent capability for high-speed tracking and levitation control.     

动态优化双估计器的多模型自适应混合控制

针对参数子集个数较多导致计算量较大和由于系统参数发生跳变造成系统暂态性能差的问题,本文提出了基于动态优化双估计器的多模型自适应混合控制方法.首先对多个参数子集进行动态优化得到最优参数子集,减少了需要计算的模型数量,提高了系统收敛速度;其次对被控对象设置一个固定初值的估计器和一个可重新赋值的估计器,固定估计器用于初始时刻对参数的估计,可赋值估计器动态调整估计初值用于减小估计误差,提高系统暂态性能.最后的仿真结果表明了该方法的有效性,并给出了系统的稳定性及收敛性分析.     

基于状态估计的摩擦模糊建模与鲁棒自适应控制

针对一类多自由度机械系统, 研究了基于状态估计的摩擦模糊建模与鲁棒自适应控制问题. 提出用模糊状态估计器估计摩擦模型中的不可测变量, 并用严格正实和李雅普诺夫稳定性理论证明了状态估计误差的一致最终有界性. 运用模糊状态估计结果设计了多变量鲁棒自适应控制器, 其中摩擦模糊模型中的自适应参数是基于李雅普诺夫稳定性理论设计的, 并证明了闭环系统跟踪误差的一致最终有界性. 本文对多自由度质量、弹簧和摩擦阻尼系统进行的仿真, 结果表明所提出的状态估计算法和自适应控制策略是有效的.     

Fault estimation for T-S fuzzy Markovian jumping systems based on the adaptive observer

The adaptive fault estimation problem is studied for a class of stochastic Markovian jumping systems (MJSs) with time delays and nonlinear parameters. By means of Takagi-Sugeno fuzzy models, the dynamics of observer error generator and the fuzzy error dynamical system are constructed. Based on the selected Lyapunov-Krasovskii functional framework, the adaptive fault estimation algorithm is proposed to enhance the rapidity and accuracy performance of fault estimation. In terms of linear matrix inequalities techniques, a sufficient condition on the existence of the adaptive observer is presented and proved. Moreover, the presented results are also extended to multiple time-delayed nonlinear MJSs. A numerical example is given at last to illustrate the effectiveness of the proposed approach.     

Stable indirect adaptive switching control for fuzzy dynamical systems based on T–S multiple models

A new indirect adaptive switching fuzzy control method for fuzzy dynamical systems, based on Takagi–Sugeno (T–S) multiple models is proposed in this article. Motivated by the fact that indirect adaptive control techniques suffer from poor transient response, especially when the initialisation of the estimation model is highly inaccurate and the region of uncertainty for the plant parameters is very large, we present a fuzzy control method that utilises the advantages of multiple models strategy. The dynamical system is expressed using the T–S method in order to cope with the nonlinearities. T–S adaptive multiple models of the system to be controlled are constructed using different initial estimations for the parameters while one feedback linearisation controller corresponds to each model according to a specified reference model. The controller to be applied is determined at every time instant by the model which best approximates the plant using a switching rule with a suitable performance index. Lyapunov stability theory is used in order to obtain the adaptive law for the multiple models parameters, ensuring the asymptotic stability of the system while a modification in this law keeps the control input away from singularities. Also, by introducing the next best controller logic, we avoid possible infeasibilities in the control signal. Simulation results are presented, indicating the effectiveness and the advantages of the proposed method.     

Adaptive fuzzy robust control of PMSM with smooth inverse based dead-zone compensation

It is a challenging work to design high precision/high performance motion controller for permanent magnet synchronous motor (PMSM) due to some difficulties, such as varying operating conditions, parametric uncertainties and external disturbances. In order to improve tracking control performance of PMSM, this paper proposes an adaptive fuzzy robust control (AFRC) algorithm with smooth inverse based dead-zone compensation. Instead of nonsmooth dead-zone inverse which would cause the possible control signal chattering phenomenon, a new smooth dead-zone inverse is proposed for non-symmetric dead-zone compensation in PMSM system. AFRC controller is synthesized by combining backstepping technique and small gain theorem. Discontinuous projectionbased parameter adaptive law is used to estimate unknown system parameters. The Takagi-Sugeno fuzzy logic systems are employed to approximate the unstructured dynamics. Robust control law ensures the robustness of closed loop control system. The proposed AFRC algorithm with smooth inverse based dead-zone compensation is verified on a practical PMSM control system. The comparative experimental results indicate that the smooth inverse for non-symmetric dead-zone nonlinearity can effectively avoid the chattering phenomenon which would be caused by nonsmooth dead-zone inverse, and the proposed control strategy can improve the PMSM output tracking performance.     

A new adaptive backstepping method for nonlinear control of turbine main steam valve

A new approach for nonlinear adaptive control of turbine main steam valve is developed. In comparison with the existing controller based on ＂classical＂ adaptive backstepping, this method does not follow the classical certaintyequivalence principle in the design of adaptive control law. We introduce this approach, for the first time, to power systems and present a novel parameter estimator and dynamic feedback controller for a single machine infinite bus （SMIB） system with steam valve control. This system contains unknown parameters such as reactance of transmission lines. Besides preserving useful nonlinearities and the real-time estimation of uncertain parameters, the proposed approach possesses better performances with respect to the response of the system and the speed of adaptation. The simulation results demonstrate that the proposed approach is better than the design based on ＂classical＂ adaptive backstepping in terms of properties of stability and parameter estimation, and recovers the performance of the ＂full-information＂ controller. Hence, the proposed method provides an alternative for engineers in applications.     

Robust adaptive trajectory tracking control of underactuated autonomous underwater vehicles with prescribed performance

In this paper, a novel robust adaptive trajectory tracking control scheme with prescribed performance is developed for underactuated autonomous underwater vehicles (AUVs) subject to unknown dynamic parameters and disturbances. A simple error mapping function is proposed in order to guarantee that the trajectory tracking error satisfies the prescribed performance. A novel additional control based on Nussbaum function is proposed to handle the underactuation of AUVs. The compounded uncertain item caused by the unknown dynamic parameters and disturbances is transformed into a linear parametric form with only single unknown parameter called virtual parameter. On the basis of the above, a novel robust adaptive trajectory tracking control law is developed using dynamic surface control technique, where the adaptive law online provides the estimation of the virtual parameter. Strict stability analysis indicates that the designed control law ensures uniform ultimate boundedness of the AUV trajectory tracking closed‐loop control system with prescribed tracking performance. Simulation results on an AUV in two different disturbance cases with dynamic parameter perturbation verify the effectiveness of our adaptive trajectory tracking control scheme.     

Hybrid adaptive fuzzy identification and control of nonlinearsystems

We present a combined direct and indirect adaptive control scheme for adjusting an adaptive fuzzy controller, and adaptive fuzzy identification model parameters. First, using adaptive fuzzy building blocks, with a common set of parameters, we design and study an adaptive controller and an adaptive identification model that have been proposed for a general class of uncertain structure nonlinear dynamic systems. We then propose a hybrid adaptive (HA) law for adjusting the parameters. The HA law utilizes two types of errors in the adaptive system, the tracking error and the modeling error. Performance analysis using a Lyapunov synthesis approach proves the superiority of the HA law over the direct adaptive (DA) method in terms of faster and improved tracking and parameter convergence. Furthermore, this is achieved at negligible increased implementation cost or computational complexity. We prove a theorem that shows the properties of this hybrid adaptive fuzzy control system, i.e., bounds for the integral of the squared errors, and the conditions under which these errors converge asymptotically to zero are obtained. Finally, we apply the hybrid adaptive fuzzy controller to control a chaotic system, and the inverted pendulum system     

基于扰动补偿的无微分模型参考自适应控制系统设计

针对一类含有参数不确定性和未知非线性扰动的系统,本文提出一种基于扰动补偿的无微分模型参考自适应控制方法,实现系统输出对参考模型输出信号的高精度跟踪.首先,利用被控对象模型信息设计扰动估计器,对系统非线性扰动进行在线估计;其次,基于非线性扰动估计值设计参考模型和无微分参数更新律,构建无微分模型参考自适应控制器,建立基于扰动补偿和状态反馈的自适应控制律,以消除参数不确定性和非线性扰动对系统输出的影响,保证系统输出对参考模型输出的准确跟踪;然后,给出闭环系统误差信号收敛条件和控制器参数整定方法;最后,通过数值仿真验证所提方法的有效性和优越性.     

Takagi-Sugeno fuzzy model based indirect adaptive fuzzy observer and controller design

This paper proposes the design scheme of the alternative adaptive observer and controller based on the Takagi-Sugeno (T-S) fuzzy model. The T-S fuzzy modeling and the state feedback control technique are adopted for the simple structure. The proposed method maintains consistent performance in the presence of parameter uncertainties and incorporates linguistic fuzzy information from human operators. In addition, with the simple adaptive state feedback controller, it solves the singularity problem, which occurs in the inverse dynamics based on the feedback linearization method. Using Lyapunov theory and Lipschitz condition, the stability analysis is conducted, and the adaptive law is derived. The proposed method is applied to the stabilization problem of a flexible joint manipulator in order to guarantee its performance.     

Adaptive controller design for uncertain fuzzy systems using variable structure control approach

Based on the variable structure control (VSC) theory, we develop an adaptive fuzzy control system design method for uncertain Takagi-Sugeno fuzzy models with norm-bounded uncertainties. We relax the restrictive assumptions that each nominal local system model shares the same input channel and the norm bound of the uncertainty is known, which are usually invoked in the traditional VSC-based fuzzy control design methods. As the local controller we use a VSC law with a switching feedback control term and an adaptation law to account for the norm-bounded uncertainties. In terms of LMIs, we derive a sufficient condition for the existence of linear sliding surfaces guaranteeing the asymptotic stability. We present an LMI characterization of such sliding surfaces. We also give an LMI-based design algorithm, together with a numerical design example.     

Sigma adaptive fuzzy sliding mode control of a class of nonlinear systems

Based on fuzzy approximators of nonlinear functions, a new adaptive fuzzy sliding mode control scheme is proposed for a class of nonlinear plants. In comparison with most existing methods, in which the parameter projection algorithm is often involved to prevent the estimated value of the input gain function from evolving into zero, the proposed control law has shown its success and simplicity in tackling the case when the value of the estimated input gain function becomes zero during online operations. A variant of adaptive law with dead-zone sigma-modification is introduced to help achieve this goal. The bounding parameters of the model approximation error and the external disturbance are all regarded as unknown constants in this paper, and adaptive laws for them are devised for tracking purposes. Based on Lyapunov's stability theory the proposed controller has been shown to render the tracking error arbitrarily close to zero. A comparably good tracking performance is obtained as illustrated by the simulation results for an inverted pendulum system.     

A new T-S fuzzy model predictive control for nonlinear processes

In this paper, a novel fuzzy Generalized Predictive Control (GPC) is proposed for discrete-time nonlinear systems via Takagi-Sugeno system based Kernel Ridge Regression (TS-KRR). The TS-KRR strategy approximates the unknown nonlinear systems by learning the Takagi-Sugeno (TS) fuzzy parameters from the input-output data. Two main steps are required to construct the TS-KRR: the first step is to use a clustering algorithm such as the clustering based Particle Swarm Optimization (PSO) algorithm that separates the input data into clusters and obtains the antecedent TS fuzzy model parameters. In the second step, the consequent TS fuzzy parameters are obtained using a Kernel ridge regression algorithm. Furthermore, the TS based predictive control is created by integrating the TS-KRR into the Generalized Predictive Controller. Next, an adaptive, online, version of TS-KRR is proposed and integrated with the GPC controller resulting an efficient adaptive fuzzy generalized predictive control methodology that can deal with most of the industrial plants and has the ability to deal with disturbances and variations of the model parameters. In the adaptive TS-KRR algorithm, the antecedent parameters are initialized with a simple K-means algorithm and updated using a simple gradient algorithm. Then, the consequent parameters are obtained using the sliding-window Kernel Recursive Least squares (KRLS) algorithm. Finally, two nonlinear systems: A surge tank and Continuous Stirred Tank Reactor (CSTR) systems were used to investigate the performance of the new adaptive TS-KRR GPC controller. Furthermore, the results obtained by the adaptive TS-KRR GPC controller were compared with two other controllers. The numerical results demonstrate the reliability of the proposed adaptive TS-KRR GPC method for discrete-time nonlinear systems.