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.     

A new model-free adaptive sliding controller for active suspension system

Active suspension systems are designed to provide better ride comfort and handling capability in the automotive industry. Since the active suspension system has nonlinear and time-varying characteristics, it is difficult to establish an accurate dynamic model for designing a model-based controller. Here, a functional approximation (FA) based adaptive sliding controller with fuzzy compensation is proposed for an active suspension system. The FA technique is employed to represent the unknown functions, which releases the model-based requirement of the sliding mode control. In addition, a fuzzy control scheme with online learning ability is employed to compensate for the modeling error of the FA with finite number of terms for reducing the implementation difficulty. To guarantee the control system stability, the update laws of the coefficients in the approximation function and the fuzzy tuning parameters are derived from the Lyapunov theorem. The proposed controller is employed on a quarter-car active suspension system. The simulation results and experimental results show that the proposed controller can suppress the oscillation amplitude of the sprung mass effectively. To evaluate the performance improvement of inducing a fuzzy compensator in this FA adaptive controller, the dynamic responses of the proposed hybrid controller are compared with those of FA-based adaptive sliding controller only.     

Adaptive fuzzy identification and predictive control for industrial processes

This paper proposes a method for adaptive identification and control for industrial applications. The learning of a T–S fuzzy model is performed from input/output data to approximate unknown nonlinear processes by a hierarchical genetic algorithm (HGA). The HGA approach is composed by five hierarchical levels where the following parameters of the T–S fuzzy system are learned: input variables and their respective time delays, antecedent fuzzy sets, consequent parameters, and fuzzy rules. In order to reduce the computational cost and increase the algorithm’s performance an initialization method is applied on HGA. To deal with nonlinear plants and time-varying processes, the T–S fuzzy model is adapted online to maintain the quality of the identification/control. The identification methodology is proposed for two application problems: (1) the design of data-driven soft sensors, and (2) the learning of a model for the Generalized predictive control (GPC) algorithm. The integration of the proposed adaptive identification method with the GPC results in an effective adaptive predictive fuzzy control methodology. To validate and demonstrate the performance and effectiveness of the proposed methodologies, they are applied on identification of a model for the estimation of the flour concentration in the effluent of a real-world wastewater treatment system; and on control of a simulated continuous stirred tank reactor (CSTR) and on a real experimental setup composed of two coupled DC motors. The results are presented, showing that the developed evolving T–S fuzzy model can identify the nonlinear systems satisfactorily and it can be used successfully as a prediction model of the process for the GPC controller.     

Adaptive fuzzy controller with sliding surface for vehicle suspension control

Since the hydraulic actuating suspension system has nonlinear and time-varying behavior, it is difficult to establish an accurate model for designing a model-based controller. Here, an adaptive fuzzy sliding mode controller is proposed to suppress the sprung mass position oscillation due to road surface variation. This intelligent control strategy combines an adaptive rule with fuzzy and sliding mode control algorithms. It has online learning ability to deal with the system time-varying and nonlinear uncertainty behaviors, and adjust the control rules parameters. Only eleven fuzzy rules are required for this active suspension system and these fuzzy control rules can be established and modified continuously by online learning. The experimental results show that this intelligent control algorithm effectively suppresses the oscillation amplitude of the sprung mass with respect to various road surface disturbances.     

GA-based modified adaptive fuzzy sliding mode controller for nonlinear systems

In this paper, the stability analysis of the GA-based adaptive fuzzy sliding model controller for a nonlinear system is presented. First, an uncertain and nonlinear plant for the tracking of a reference trajectory is well approximated and described via the reference model and the fuzzy model involving fuzzy logic control rules. Next, the difficulty in designing a fuzzy sliding mode controller (FSMC) capable of rapidly and efficiently controlling complex and nonlinear systems is how to select the most appropriate initial values for the parameter vector. The initial values of the consequent parameter vector are decided via the genetic algorithm. After this, a modified adaptive law can be adopted to find the best high-performance parameters for the fuzzy sliding model controller. The adaptive fuzzy sliding model controller is derived to simultaneously stabilize and control the system. The stability of the nonlinear system is ensured by the derivation of the stability criterion based upon Lyapunov’s direct method. Finally, a numerical simulation is provided as an example to demonstrate the control methodology.     

Stable fuzzy neural tracking control of a class of unknown nonlinear systems based on fuzzy hierarchy error approach

In this paper, a stable fuzzy neural tracking control of a class of unknown nonlinear systems based on the fuzzy hierarchy approach is proposed. The adaptive fuzzy neural controller is constructed from the fuzzy neural network with a set of fuzzy rules. The corresponding network parameters are adjusted online according to the control law and update law for the purpose of controlling the plant to track a given trajectory. A stability analysis of the unknown nonlinear system is discussed based on the Lyapunov principle. In order to improve the convergence of the nonlinear dynamical systems, a fuzzy hierarchy error approach (FHEA) algorithm is incorporated into the adaptive update and control scheme. The simulation results for an unstable nonlinear plant demonstrate the control effectiveness of the proposed adaptive fuzzy neural controller and are consistent with the theoretical analysis.     

An Indirect Adaptive Fuzzy Control Scheme for a Class of Nonlinear Systems

This paper presents an indirect adaptive control scheme, for a class of nonlinear systems in controller canonical form. Owing to the universal approximation property of a Takagi–Sugeno (T–S) fuzzy model, controller design is simplified by utilizing the T–S fuzzy model representation of a nonlinear system. An adaptation mechanism ensures that the estimator model asymptotically follow the actual T–S fuzzy model and thus removes the need of any a priori identification of the T–S fuzzy model of the system. The overall controller gain is a convex combination of the local linear gains which vary adaptively to ensure the convergence of the tracking error. Preliminary simulation results indicate the potential of the proposed method.     

T-S model based indirect adaptive fuzzy control using online parameter estimation

A parameter estimation scheme with an appropriate adaptive law for updating the parameters is designed and analyzed based on the Lyapunov theory for the general MIMO Takagi-Sugeno (T-S) fuzzy models. The parameters of the Takagi-Sugeno fuzzy models can be estimated by observing the behavior of the system and with the online parameter estimator, any type of fuzzy controllers works adaptively to the parameter perturbation. In order to show the applicability of the proposed estimator, an existing fuzzy state feedback controller is adopted and indirect adaptive fuzzy control design with the proposed estimator is shown. From the numerical simulations and experiments, it is shown that the derived adaptive law works for the estimation model to follows the parameterized plant model and the overall control system has robustness to the parameter perturbation.     

Fuzzy dynamic characteristic modeling and adaptive control of nonlinear systems and its application to hypersonic vehicles

In this paper, a fuzzy dynamic characteristic modeling and adaptive control method is proposed for a class of nonlinear systems. By employing fuzzy dynamic characteristic model, the controlled plant is described as a slowly time-varying fuzzy system, wherein the parameters are estimated online by using recursive Least-Squares algorithm. Under this framework, a fuzzy adaptive controller is constructed, and the stability condition of the closed-loop system is also derived. The main advantage of the proposed m...     

Adaptive Fuzzy Switched Swing-Up and Sliding Control for the Double-Pendulum-and-Cart System

In this paper, an adaptive fuzzy switched swing-up and sliding controller (AFSSSC) is proposed for the swing-up and position controls of a double-pendulum-and-cart system. The proposed AFSSSC consists of a fuzzy switching controller (FSC), an adaptive fuzzy swing-up controller (FSUC), and an adaptive hybrid fuzzy sliding controller (HFSC). To simplify the design of the adaptive HFSC, the double-pendulum-and-cart system is reformulated as a double-pendulum and a cart subsystem with matched time-varying uncertainties. In addition, an adaptive mechanism is provided to learn the parameters of the output fuzzy sets for the adaptive HFSC. The FSC is designed to smoothly switch between the adaptive FSUC and the adaptive HFSC. Moreover, the sliding mode and the stability of the fuzzy sliding control systems are guaranteed. Simulation results are included to illustrate the effectiveness of the proposed AFSSSC.      

An indirect model reference robust fuzzy adaptive control for a class of SISO nonlinear systems

In this paper we are interested in robust adaptive fuzzy control of nonlinear SISO systems in the presence of parametric uncertainties. The plant model structure is represented by the Takagi-Sugeno (T-S) type fuzzy system. An indirect adaptive fuzzy controller based on model reference control scheme is proposed to provide asymptotic tracking of reference signal. The controller parameters are computed at each time. The plant state tracks asymptotically the state of the reference model for any bounded reference input signal. Inverted pendulum and mass spring damper are used to check the performance of the proposed controller.     

具有未知非线性死区的自适应模糊控制

基于滑模控制原理，利用模糊系统的逼近能力，提出一种自适应模糊控制方法．该方法提出一种简化非线性死区输入模型，取消了非线性死区输入模型的倾斜度相等以及死区边界对称的条件，还取消了非线性死区输入模型各种参数已知的条件．该方法通过引入逼近误差的自适应补偿项来消除建模误差和参数估计误差的影响．理论分析证明了闭环系统是半全局一致终结有界，跟踪误差收敛到零．仿真结果表明了该方案的有效性．     

Adaptive fuzzy terminal sliding mode controller for linear systems with mismatched time-varying uncertainties

A new design approach of an adaptive fuzzy terminal sliding mode controller for linear systems with mismatched time-varying uncertainties is presented in this paper. A fuzzy terminal sliding mode controller is designed to retain the advantages of the terminal sliding mode controller and to reduce the chattering occurred with the terminal sliding mode controller. The sufficient condition is provided for the uncertain system to be invariant on the sliding surface. The parameters of the output fuzzy sets in the fuzzy mechanism are adapted on-line to improve the performance of the fuzzy sliding mode control system. The bounds of the uncertainties are not required to be known in advance for the presented adaptive fuzzy sliding mode controller. The stability of the fuzzy control system is also guaranteed. 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 adaptive fuzzy terminal sliding mode controller.     

Adaptive sliding mode controller design based on T-S fuzzy system models

An adaptive sliding mode control (ASMC) technique based on T-S fuzzy system models is proposed in this paper for a class of perturbed nonlinear MIMO dynamic systems in order to solve tracking problems. A T-S fuzzy model is firstly formed by utilizing fuzzy theorem to amalgamate a set of linearized dynamic equations. The adaptive sliding mode controller is then designed based on this fuzzy model with perturbations. The proposed control scheme can drive the dynamics of controlled system into a designated sliding surface in finite time, and guarantee the property of asymptotical stability. It is also shown that the information of upper bound of modeling errors as well as perturbations, except the information of upper bound of input uncertainty, is not required when using the proposed controller.     

利用模糊系统的直升机的自适应控制

针对直升机动力学为非线性,且存在不确定因素和状态变化,设计利用模糊系统的自适应控制器.设计的控制器是系统的输出跟踪参考模型输出的直接调整模糊控制器参数的自适应控制器.又利用Lyapunov函数保证了闭环控制系统的稳定性并推导最优的自适应规律.实验结果表明,有外部扰动的情况下所设计的自适应控制器比模糊控制器对直升机控制具有良好的动态响应和稳定性,是一种非常有效的控制方法.     

PHANTOM Omni机器人的自适应模糊滑模控制

针对PHANTOM Omni机器人的位置轨迹跟踪问题,采用了一种基于模糊逻辑的自适应模糊滑模控制方案。利用滑模控制中的切换函数作为输入,根据模糊系统的逼近能力设计控制器,并基于李雅谱诺夫方法设计自适应律对控制器所需参数进行实时调节。仿真中将其与传统的滑模控制进行了比较,仿真结果表明：自适应模糊滑模控制能使PHANTOM Omni机器人更好地实现期望的位置轨迹跟踪并有效地减轻抖振现象,从而证明了该方法在PHANTOM Omni机器人上实施的可行性。     

利用模糊系统的自适应模糊控制器

针对非线性系统控制,设计了利用TSK(Takagi-Sugeno-Kang)模糊系统的自适应模糊控制器。所设计的自适应控制方法是参考模型自适应控制方法,而且利用Lyapunov函数保证了闭环系统的稳定性,同时推导了最优的自适应控制规律。首先,根据控制对象的输入输出数据建立TSK模糊模型,然后,由TSK模糊模型设计初期的TSK模糊控制器,并根据自适应规律随时调整模糊控制器参数。倒立摆系统的仿真实验验证了所设计的自适应模糊控制器的有效性。     

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.     

基于Backstepping的高超声速飞行器模糊自适应控制

提出了高超声速飞行器的模糊自适应控制方法.根据飞行器纵向模型的特点,分别设计了基于动态逆的速度控制器和基于Backstepping的高度控制器,模糊自适应系统用来在线辨识飞行器模型由于气动参数的变化而引起的不确定性,采用Lyapunov理论设计的自适应律保证了系统的稳定性与指令跟踪的精确性.仿真使用了高超声速飞行器的纵向模型对算法进行了验证,得到了较满意的控制效果.     

Online learning in adaptive neurocontrol schemes with a slidingmode algorithm

The novel features of an adaptive PID-like neurocontrol scheme for nonlinear plants are presented. The controller tuning is based on an estimate of the command-error on its output by using a neural predictive model. A robust online learning algorithm, based on the direct use of sliding mode control (SMC) theory is applied. The proposed approach allows handling of the plant-model mismatches, uncertainties and parameters changes. The results show that both the plant model and the controller inherit some of the advantages of SMC, such as high speed of learning and robustness.