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.     

Robust decentralized adaptive fuzzy control for a class of large‐scale MIMO nonlinear systems

In this paper, a novel decentralized robust adaptive fuzzy control scheme is proposed for a class of large‐scale multiple‐input multiple‐output uncertain nonlinear systems. By virtue of fuzzy logic systems and the regularized inverse matrix, the decentralized robust indirect adaptive fuzzy controller is developed such that the controller singularity problem is addressed under a united design framework; no a priori knowledge of the bounds on lumped uncertainties are being required. The closed‐loop large‐scale system is proved to be asymptotically stable. Simulation results confirmed the validity of the approach presented. Copyright © 2011 John Wiley & Sons, Ltd.     

一种简化的自适应模糊动态面控制

针对一类不确定非线性时变时滞系统,提出了一种简化的自适应模糊动态面控制方法.该方法取消了对系统时滞常做的假设.仅采用一个模糊逼近器便使所有的未知函数得到补偿,简化了控制器的结构.通过构造合适的Lyapunov-Krasovskii泛函,闭环系统的所有信号被证明为半全局一致最终有界.仿真实例进一步验证了控制方案的有效性.     

Adaptive fuzzy tracking control of nonlinear time-delay systems with unknown virtual control coefficients

In this paper, a novel adaptive fuzzy control scheme is proposed for a class of uncertain single-input and single-output (SISO) nonlinear time-delay systems with the lower triangular form. Fuzzy logic systems are used to approximate unknown nonlinear functions, then the adaptive fuzzy tracking controller is constructed by combining Lyapunov-Krasovskii functionals and the backstepping approach. The proposed controller guarantees uniform ultimate boundedness of all the signals in the closed-loop system, while the tracking error converges to a small neighborhood of the origin. An advantage of the proposed control scheme lies in that the number of adaptive parameters is not more than the order of the systems under consideration. Finally, simulation studies are given to demonstrate the effectiveness of the proposed design 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.     

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.     

Robust adaptive fuzzy VSS control for a class of uncertain nonlinear systems using small gain design

In this paper, a novel robust adaptive fuzzy variable structure control (RAFVSC) scheme is proposed for a class of uncertain nonlinear systems. The uncertain nonlinear system and gain functions originating from modeling errors and external disturbances are all unstructured (or non-repeatable), state-dependent and completely unknown. The Takagi–Sugeno type fuzzy logic systems are used to approximate uncertain functions in the systems and the RAFVSC is designed by use of the input-to-state stability (ISS) approach and small gain theorem. In the algorithm, there are three advantages which are that the asymptotic stability of adaptive control in the presence of unstructured uncertainties can be guaranteed, the possible controller singularity problem in some of existing adaptive control schemes using feedback linearization techniques can be removed and the adaptive mechanism with minimal learning parameterizations can be achieved. The performance and effectiveness of the proposed methods are discussed and illustrated with two simulation examples.     

一类非线性离散系统模糊控制器的分析和设计

针对一类非线性离散不确定系统,在系统状态不可测的情况下,以T-S模型描述不同状态空间的局部动态区域,并通过中心平均反模糊化、乘积推理、单点模糊化方法得到全局模糊系统模型.基于李亚普诺夫理论和线性矩阵不等式,设计了一种基于观测器的鲁棒控制器,并对离散状态下的此类系统进行了稳定分析.最后通过M ATLAB仿真,证明了该方法的有效性.     

基于动态面的高超声速飞行器模糊自适应非线性控制

针对高超声速飞行器模型非线性、多变量和参数不确定特性, 并考虑控制增益变化可能导致控制奇异值问 题, 提出一种基于动态面的模糊自适应非线性控制方法. 根据动态面和动态逆策略, 分别设计了高度和速度跟踪控制 器. 利用模糊自适应方法在线逼近不确定函数项, 并采用Nussbaum 增益技术抑制虚拟控制增益不确定影响, 以减少 在线学习量, 保证系统的半全局一致最终有界性. 仿真结果表明, 所提出的方法可实现飞行器对高度和速度的准确跟 踪控制.

     

Adaptive fuzzy control of MIMO nonlinear systems with fuzzy dead zones

In this paper, the problem of adaptive fuzzy tracking control is investigated for a class of multi-input multi-output nonlinear systems with fuzzy dead zones. The virtual control gain functions and uncertain functions considered in the studied system are all unknown. Fuzzy logic systems are employed to approximate the unknown functions. With the combination of adaptive backstepping design technique and dynamic surface control method, the problem caused by differentiating nonlinear functions repeatedly is avoided. Furthermore, only one adaptive parameter needs to be updated online for each subsystem, which reduces the computation burden considerably. The presented controller not only guarantees the desired control performance, but also guarantees the boundedness of all closed-loop signals. Simulation results are shown to demonstrate the effectiveness of the proposed algorithm.     

Adaptive fuzzy backstepping output feedback control of nonlinear uncertain systems with unknown virtual control coefficients using MT-filters

In this paper, an adaptive fuzzy output feedback control approach is developed for a class of SISO nonlinear uncertain systems with unmeasured states and unknown virtual control coefficients. The fuzzy logic systems are used to model the uncertain nonlinear systems. The MT-filters and the state observer are designed to estimate the unmeasured states. Using backstepping design principle and combining the Nussbaum gain functions, an adaptive fuzzy output feedback control scheme is developed. It is proved that the proposed adaptive fuzzy control approach can guarantee all the signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error converges to a small neighborhood of origin. A simulation is included to illustrate the effectiveness of the proposed approach.     

Observer-based hybrid adaptive fuzzy control for affine and nonaffine uncertain nonlinear systems

This paper presents a novel observer-based hybrid adaptive fuzzy controller for affine and nonaffine nonlinear systems with external disturbance. The suggested design is so easy and does not need a mathematical model for system under control and also it is very simple, efficient and robust. Based on the adaptive method and the system states observer, an observer-based adaptive fuzzy method is proposed to control an uncertain nonlinear system. Also, a supervisory controller term is employed to attenuate the residual error to a desired level and compensate the both uncertainties and observer errors. Although proposed control method needs the uncertainties to be bounded, it does not need this bound to be identified. Stability of the proposed method is shown based on Lyapunov theory and also the strictly positive real condition if all the implicated signals are uniformly bounded. Finally, in our simulation studies, to demonstrate the usefulness and efficiency of the suggested technique, an uncertain nonlinear system is employed.

     

Distributed Adaptive Dynamic Surface Control for Synchronization of Uncertain Nonlinear Multi-agent Systems

In this paper a distributed adaptive dynamic surface controller is proposed for multi-agent systems under fixed directed graph topologies. The agents have uncertain nonlinear dynamics and are influenced by bounded unknown disturbances. The controller should synchronize the states of all agents with the corresponding states of the nonautonomous leader. It is proved that, with the proposed controller, the synchronization error remains bounded; and the bounds can be arbitrarily decreased by increasing the controller gains. The control rules are designed such that each agent only requires the state information of its neighbors, rendering a distributed control. The effectiveness of the proposed method is demonstrated through two simulation examples.     

一类MIMO非线性大系统基于H∞ 跟踪的分散自适应输出反馈模糊控制

针对一类状态不可测的MIMO不确定非线性大系统,提出一种基于H∞跟踪的分散自适应输出反馈模糊控制器.主要工作有:1)通过对观测误差向量进行滤波来确保严格正实条件成立,使得提出的反馈与自适应机制可以执行;2)利用模糊系统提出一种适用于一般非线性大系统基于H∞跟踪的分散自适应模糊控制方案;3)在统一的框架下处理了控制器奇异性.闭环大系统被证明足稳定的,且输出误差具有H∞跟踪性能.仿真结果验证了控制器设计的有效性.     

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.     

Robust Decentralized Adaptive Fuzzy Control of Large‐Scale Nonaffine Nonlinear Systems With Strong Interconnection and Application to Automated Highway Systems

A novel decentralized adaptive fuzzy controller is developed for a class of large‐scale uncertain nonaffine nonlinear systems in this paper. Incorporating the benefits of fuzzy systems, implicit function theorem, and robust control technique, the interconnections between subsystems are extended to general unknown nonlinear functions. No a priori knowledge of lower and upper bounds on lumped uncertainties is required to implement each local controller. The resulting closed‐loop large‐scale system is proved to be asymptotically stable. The controller design is applicable to an automated highway system and simulation results confirm its practical usefulness.     

Direct adaptive fuzzy control for nonlinear systems with time-varying delays

This paper focuses on the problem of direct adaptive fuzzy control for nonlinear strict-feedback systems with time-varying delays. Based on the Razumikhin function approach, a novel adaptive fuzzy controller is designed. The proposed controller guarantees that the system output converges to a small neighborhood of the reference signal and all the signals in the closed-loop system remain bounded. Different from the existing adaptive fuzzy control methodology, the fuzzy logic systems are used to model the desired but unknown control signals rather than the unknown nonlinear functions in the systems. As a result, the proposed adaptive controller has a simpler form and requires fewer adaptation parameters.     

An adaptive full order sliding mode controller for mismatched uncertain systems

In this paper, an adaptive full order sliding mode (FOSM) controller is proposed for strict feedback nonlinear systems with mismatched uncertainties. The design objective of the controller is to track a specified trajectory in presence of significant mismatched uncertainties. In the first step the dynamic model for the first state is considered by the desired tracking signal. After the first step the desired dynamic model for each state is defined by the previous one. An adaptive tuning law is developed for the FOSM controller to deal with the bounded system uncertainty. The major advantages offered by this adaptive FOSM controller are that advanced knowledge about the upper bound of the system uncertainties is not a necessary requirement and the proposed method is an effective solution for the chattering elimination from the control signal. The controller is designed considering the full-order sliding surface. System robustness and the stability of the controller are proved by using the Lyapunov technique. A systematic adaptive step by step design method using the full order sliding surface for mismatched nonlinear systems is presented. Simulation results validate the effectiveness of the proposed control law.     

Indirect adaptive fuzzy control for a class of nonaffine nonlinear systems with unknown control directions

This article presents an indirect adaptive fuzzy control scheme for a class of nonlinear uncertain nonaffine systems with unknown control directions. The nonlinear nonaffine system is first transformed into an affine form by using a Taylor series expansion, and then fuzzy systems are employed to approximate the equivalent affine system’s unknown nonlinearities. By modifying the estimated input control gain and using a novel smooth robust control term, a stable well-defined adaptive controller is proposed. Simulation results are provided to illustrate the efficiency of the proposed scheme.     

Adaptive neural network dynamic surface control for a class of nonlinear systems with uncertain time delays

This paper presents a solution to tracking control problem for a class of nonlinear systems with unknown parameters and uncertain time-varying delays. A new adaptive neural network(NN) dynamic surface controller(DSC) is developed. Some assumptions on uncertain time delays, which were required to be satisfied in previous works, are removed by introducing a novel indirect neural network algorithm into dynamic surface control framework. Also, the designed controller is independent of the time delays. Moreover,the dynamic compensation terms are introduced to facilitate the controller design. It is shown that the closed-loop tracking error converges to a small neighborhood of zero. Finally, a chaotic circuit system is initially bench tested to show the effectiveness of the proposed method.