Robust adaptive fuzzy tracking control for a class of strict-feedback nonlinear systems based on backstepping technique

In this paper, the robust adaptive fuzzy tracking control problem is discussed for a class of perturbed strict-feedback nonlinear systems. The fuzzy logic systems in Mamdani type are used to approximate unknown nonlinear functions. A design scheme of the robust adaptive fuzzy controller is proposed by use of the backstepping technique. The proposed controller guarantees semi-global uniform ultimate boundedness of all the signals in the derived closed-loop system and achieves the good tracking performance. The possible controller singularity problem which may occur in some existing adaptive control schemes with feedback linearization techniques can be avoided. In addition, the number of the on-line adaptive parameters is not more than the order of the designed system. Finally, two simulation examples are used to demonstrate the effectiveness of the proposed control scheme.     

Robust adaptive fuzzy tracking control for a class of strict-feedback nonlinear systems based on backstepping technique

In this paper, the robust adaptive fuzzy tracking control problem is discussed for a class of perturbed strict-feedback nonlinear systems. The fuzzy logic systems in Mamdani type are used to approximate unknown nonlinear functions. A design scheme of the robust adaptive fuzzy controller is proposed by use of the backstepping technique. The proposed controller guarantees semi-global uniform ultimate boundedness of all the signals in the derived closed-loop system and achieves the good tracking performance. The possible controller singularity problem which may occur in some existing adaptive control schemes with feedback linearization techniques can be avoided. In addition, the number of the on-line adaptive parameters is not more than the order of the designed system. Finally, two simulation examples are used to demonstrate the effectiveness of the proposed control scheme.     

Robust adaptive self-structuring fuzzy control design for nonaffine,nonlinear systems

In this article, a robust adaptive self-structuring fuzzy control (RASFC) scheme for the uncertain or ill-defined nonlinear, nonaffine systems is proposed. The RASFC scheme is composed of a robust adaptive controller and a self-structuring fuzzy controller. In the self-structuring fuzzy controller design, a novel self-structuring fuzzy system (SFS) is used to approximate the unknown plant nonlinearity, and the SFS can automatically grow and prune fuzzy rules to realise a compact fuzzy rule base. The robust adaptive controller is designed to achieve an L ₂ tracking performance to stabilise the closed-loop system. This L ₂ tracking performance can provide a clear expression of tracking error in terms of the sum of lumped uncertainty and external disturbance, which has not been shown in previous works. Finally, five examples are presented to show that the proposed RASFC scheme can achieve favourable tracking performance, yet heavy computational burden is relieved.     

基于分层模糊系统的直接自适应控制

为解决模糊控制器中规则数目随系统变量呈指数增长的问题，利用分层模糊系统设计了一类非线性系统的直接自适应模糊控制器，并证明了所提出的设计方法不但能保证闭环系统的一致有界性。而且可使跟踪误差收敛到原点的小领域内，通过对倒立摆控制的仿真研究验证了该方法的有效性。     

Adaptive fuzzy control for pure-feedback stochastic nonlinear systems with unknown dead-zone input

This paper is concerned with the problem of adaptive fuzzy output tracking control for a class of nonlinear pure-feedback stochastic systems with unknown dead-zone. Fuzzy logic systems in Mamdani type are used to approximate the unknown nonlinearities, then a novel adaptive fuzzy tracking controller is designed by using backstepping technique. The control scheme is systematically derived without requiring any information on the boundedness of dead-zone parameters (slopes and break-points) and the repeated differentiation of the virtual control signals. The proposed adaptive fuzzy controller guarantees that all the signals in the closed-loop system are bounded in probability and the system output eventually converges to a small neighbourhood of the desired reference signal in the sense of mean quartic value. Simulation results further illustrate the effectiveness of the proposed control scheme.     

Adaptive fuzzy control for multi-input multi-output nonlinear systems with unknown dead-zone inputs

This paper presents an adaptive fuzzy control scheme for a class of uncertain multi-input multi-output (MIMO) nonlinear systems with the nonsymmetric control gain matrix and the unknown dead-zone inputs. In this scheme, fuzzy systems are used to approximate the unknown nonlinear functions and the estimated symmetric gain matrix is decomposed into a product of one diagonal matrix and two orthogonal matrices. Based on the decomposition results, a controller is developed, therefore, the possible controller singularity problem and the parameter initialization condition constraints problem are avoided. In addition, a dynamic robust controller is employed to compensate for the lumped errors. It is proved that all the signals in the proposed closed-loop system are bounded and that the tracking errors converge asymptotically to zero. A simulation example is used to demonstrate the effectiveness of the proposed scheme.     

非线性互联系统的分散混合自适应智能控制

针对一类高阶互联MIMO非线性系统，利用TS模糊系统和神经网络的通用逼近能力，在神经网络控制器中引入模糊基函数，提出一种分散混合自适应智能控制器设计的新方案．基于等价控制思想，设计分散自适应控制器，无需计算TS模型．通过对不确定项进行自适应估计，取消了其存在已知上界的假设．通过理论分析，证明了闭环智能控制系统所有信号有界，跟踪误差收敛到零．     

Direct adaptive fuzzy control of nonlinear strict-feedback systems

This paper focuses on adaptive fuzzy tracking control for a class of uncertain single-input /single-output nonlinear strict-feedback systems. Fuzzy logic systems are directly used to approximate unknown and desired control signals and a novel direct adaptive fuzzy tracking controller is constructed via backstepping. The proposed adaptive fuzzy controller guarantees that the output of the closed-loop system converges to a small neighborhood of the reference signal and all the signals in the closed-loop system remain bounded. A main advantage of the proposed controller is that it contains only one adaptive parameter that needs to be updated online. Finally, an example is used to show the effectiveness of the proposed approach.     

基于模糊树模型的自适应模糊滑模控制方法

本文针对单输入–单输出仿射非线性系统提出了一种基于模糊树模型的具有监督控制器的模糊滑模控制方法. 该方法用模糊树模型逼近非线性系统中的未知非线性函数, 得到初始的控制器, 然后在线调节模糊树模型中的线性参数, 改善控制器的性能, 实现对有界参考输入信号的跟踪控制. 模糊树辨识方法自适应划分输入空间, 大大减少模糊规则的数目, 在一定程度上可以缓解困扰模糊控制中的”规则爆炸”问题. 该方法通过监督控制器保证闭环系统所有信号有界. 通过理论分析, 证明了跟踪误差收敛到零. 用倒立摆进行仿真验证, 结果表明该方法用较少的模糊规则, 就能得到满意的控制效果, 有推广应用价值.     

Observer-based adaptive fuzzy backstepping control of uncertain nonlinear pure-feedback systems

In this paper,a new fuzzy adaptive control approach is developed for a class of SISO uncertain pure-feedback nonlinear systems with immeasurable states.Fuzzy logic systems are utilized to approximate the unknown nonlinear functions;and the filtered signals are introduced to circumvent algebraic loop systems encountered in the implementation of the controller,and a fuzzy state adaptive observer is designed to estimate the immeasurable states.By combining the adaptive backstepping technique,an adaptive fuzzy output feedback control scheme is developed.It is proven that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded(SGUUB),and the observer and tracking errors converge to a small neighborhood of the origin by appropriate choice of the design parameters.Simulation studies are included to illustrate the efectiveness of the proposed approach.     

基于模糊逻辑系统的输出跟踪控制问题

针对一类未知的非线性互联大系统，设计间接自适应模糊控制器以实现跟踪控制，采用模糊控制，模糊逻辑逼近和模糊滑模控制相结合的方法，对维数较低的子系统未知动态和维数较高的互联项未知动态分别采用两类模糊规则进行逼近，对系统的外部干扰及模糊逼近误差采用模糊滑模控制予以抵消，基于Lyapunov方法实现模糊系统中的参数自适应律并在线调节，所设计的间接自适应控制器使系统在Lyapunov意义下稳定，且跟踪误差趋近于0，仿真结果表明了该设计方法的正确性。     

A novel adaptive control approach for nonlinear strict-feedback systems using nonlinearly parameterised fuzzy approximators

In this article, the problem of output tracking of perturbed nonlinear strict-feedback systems is addressed and a novel adaptive fuzzy control scheme is proposed. The considered systems are with unknown nonlinearities, so an adaptive fuzzy approximation approach is embedded into a backstepping procedure to get the proposed controller. However, unlike the exiting results, approximators used in this article are not linearly parameterised. Using nonlinearly parameterised adaptive fuzzy approximators, the controller can be obtained without the restriction that fuzzy basis functions of the approximators must be well defined. By managing to adapt the norm of on-line parameter vectors in the control design, the computation burden is largely reduced. The proposed controller can guarantee the stability and desired tracking performance of the closed-loop system. An example is included to demonstrate the effectiveness of the control scheme.     

一类MIMO非线性系统的直接自适应模糊滑模控制

针对一类具有下三角形函数控制增益矩阵的非线性系统, 基于滑模控制原理, 并利用Ⅱ型模糊系统的逼近能力, 提出了一种直接自适应模糊滑模控制器设计的新方案. 通过引入积分型李雅普诺夫函数及逼近误差自适应补偿项, 证明了闭环系统是全局稳定的, 跟踪误差收敛到零. 仿真结果表明了该方法的有效性.     

非对称饱和扇形输入非线性系统的自适应模糊控制

针对一类具有未知不确定性,且状态不可测的非线性系统,考虑了输入端的饱和非对称扇区非线性特性影响,提出了系统模型未知情形下基于自适应模糊观测器的跟踪控制方案,采用Lyapunov-Krasovskii函数给出了滑模控制器参数和模糊逻辑的自适应调整律.所提方法不仅可保证闭环跟踪系统的稳定性,还削弱了传统方法对模型结构的依赖...     

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.     

自适应模糊滑模控制器的设计与分析

研究一类非线性系统的自适应模糊控制问题,根据滑模控制原理并利用I型模糊系 统的逼近能力,提出了一种自适应模糊滑模控制器的设计方案.通过理论分析,证明了闭环模 糊控制系统的全局稳定的,跟踪误差可收敛到零的一个领域内.     

Stable adaptive fuzzy control for MIMO nonlinear systems

In this paper, an indirect adaptive fuzzy control scheme is presented for a class of multi-input and multi-output (MIMO) nonlinear systems whose dynamics are poorly understood. Within this scheme, fuzzy systems are employed to approximate the plant’s unknown dynamics. In order to overcome the controller singularity problem, the estimated gain matrix is decomposed into the product of one diagonal matrix and two orthogonal matrices, a robustifying control term is used to compensate for the lumped errors, and all parameter adaptive laws and robustifying control term are derived based on Lyapunov stability analysis. The proposed scheme guarantees that all the signals in the resulting closed-loop system are uniformly ultimately bounded (UUB). Moreover, the tracking errors can be made small enough if the designed parameter is chosen to be sufficiently large. A simulation example is used to demonstrate the effectiveness of the proposed control scheme.     

Direct adaptive fuzzy control for a class of MIMO nonlinear systems

This article presents a direct adaptive fuzzy control scheme for a class of uncertain continuous-time multi-input multi-output nonlinear (MIMO) dynamic systems. Within this scheme, fuzzy systems are employed to approximate an unknown ideal controller that can achieve control objectives. The adjustable parameters of the used fuzzy systems are updated using a gradient descent algorithm that is designed to minimize the error between the unknown ideal controller and the fuzzy controller. The stability analysis of the closed-loop system is performed using a Lyapunov approach. In particular, it is shown that the tracking errors are bounded and converge to a neighborhood of the origin. Simulations performed on a two-link robot manipulator illustrate the approach and exhibit its performance.     

具有模糊监督控制器的积分变结构间接自适应控制

针对一类不确定非线性系统, 基于变结构控制原理, 并利用具有非线性可调参数的模糊系统去逼近过程未知函数, 提出一种具有模糊监督控制器的积分变结构间接自适应控制方案. 该方案通过监督控制器保证闭环系统所有信号有界. 进一步, 通过引入最优逼近误差的自适应补偿项来消除建模误差的影响. 理论分析证明了跟踪误差收敛到零. 仿真结果表明了该方法的有效性.     

Direct adaptive fuzzy backstepping control of uncertain nonlinear systems in the presence of input saturation

In this paper, a novel direct adaptive fuzzy control approach is presented for uncertain nonlinear systems in the presence of input saturation. Fuzzy logic systems are directly used to tackle unknown nonlinear functions, and the adaptive fuzzy tracking controller is constructed by using the backstepping recursive design techniques. To overcome the problem of input saturation, a new auxiliary design system and Nussbaum gain functions are incorporated into the control scheme, respectively. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded (SGUUB), and the tracking error converges to a small neighborhood of the origin. A simulation example is included to illustrate the effectiveness of the proposed approach. Two key advantages of the scheme are that (i) the direct adaptive fuzzy control method is proposed for uncertain nonlinear system with input saturation by using Nussbaum function technique and (ii) The number of the online adaptive learning parameters is reduced.