Asymptotic tracking control for constrained nonstrict‐feedback MIMO nonlinear systems via parameter compensations

This paper studies the problem of adaptive fuzzy asymptotic tracking control for multiple input multiple output nonlinear systems in nonstrict‐feedback form. Full state constraints, input quantization, and unknown control direction are simultaneously considered in the systems. By using the fuzzy logic systems, the unknown nonlinear functions are identified. A modified partition of variables is introduced to handle the difficulty caused by nonstrict‐feedback structure. In each step of the backstepping design, the symmetric barrier Lyapunov functions are designed to avoid the breach of the state constraints, and the issues of overparametrization and unknown control direction are settled via introducing two compensation functions and the property of Nussbaum function, respectively. Furthermore, an adaptive fuzzy asymptotic tracking control strategy is raised. Based on Lyapunov stability analysis, the developed control strategy can effectually ensure that all the system variables are bounded, and the tracking errors asymptotically converge to zero. Eventually, simulation results are supplied to verify the feasibility of the proposed scheme.     

一种非线性系统的模糊自适应控制

针对一类非线性系统提出一种模糊自适应控制方案，设计中用模糊逻辑系统逼近非线性函数，骨于滑模原理及Ｌｙａｐｕｎｏｖ函数方法给出了闭环系统的稳定性分析。     

一类多变量非线性动态系统的模糊自适应控制

对一类非线性多变量未知动态系统，提出了一种模糊处在适应控制策略。证明了该控制算法能保证闭环系统稳定，跟踪误差收敛。     

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.     

一类非线性系统的自适应模糊控制

针对一类非线性系统,利用模糊推理系统对非线性函数的逼近能力,导出基于Ｌｙａｐｕｎｏｖ稳定性理论的自适应控制器,不但能解决这类非线性系统的跟踪问题,而且可保证闭环系统的稳定性。仿真结果表明这一算法的有效性。     

多输入多输出非线性多时滞系统的直接自适应模糊跟踪控制

针对多输入多输出非线性多时滞系统,提出了一种直接自适应模糊跟踪控制方案．该方案有机综合了自适应控制和H∞ 控制,构建了一种自适应时滞模糊逻辑系统用来逼近有多重时滞的未知函数;设计了H∞ 补偿器来抵消模糊逼近误差和外部扰动．根据跟踪误差给出了参数调节规律,构造了包含时滞的李亚普诺夫函数,从而证明了误差闭环系统满足期望的H∞ 跟踪性能．仿真结果表明了该方案的可行性．     

多输入多输出多重时延非线性系统的自适应模糊控制

针对多输入多输出多重时延非线性系统,提出了一种自适应模糊跟踪控制方案．该方案有机综合了自适应控制和H∞控制.文中构建了一种自适应时延模糊逻辑系统用来逼近有多重时延的未知函数;设计了H∞补偿器来抵消模糊逼近误差和外部扰动．根据跟踪误差给出了参数调节规律．构造了包含时延的李雅普诺夫函数,从而证明了误差闭环系统满足期望的H∞跟踪性能．仿真结果表明了该方案的可行性．     

Balancing control energy and tracking error for fuzzy rule emulated adaptive controller

In this article, an adaptive controller, which can minimize both tracking error and control energy, is introduced by fuzzy rule emulated network (FREN) for a class of non-affine discrete time systems. The controlled plant can be assumed as fully unknown system dynamic. Only the estimated boundary of pseudo partial derivative (PPD) is required for an on-line learning phase. The update law is derived to guarantee the convergence of tuned parameters. Lyapunov techniques are utilized to demonstrate the performance of a closed-loop system regarding the integration of the infinite cost function. The computer simulation and electronic circuit system validate the effectiveness of the proposed control scheme.     

An Adaptive Control Using Fuzzy Basis Function Expansions for a Class of Nonlinear Systems

An adaptive control using fuzzy basis function expansions is proposed for a class of nonlinear systems in this paper. It is shown that two system uncertainty bounds are approximated in a compact set by using fuzzy basis function expansion networks in the Lyapunov sense, and the outputs of the fuzzy networks are then used as the parameters of the controller to adaptively compensate for the effects of system uncertainties. Using this scheme, not only strong robustness with respect to unknown system dynamics and nonlinearities can be obtained, but also the output tracking error between the plant output and the desired reference output can be guaranteed to asymptotically converge to zero. Simulation results are provided to demonstrate the effectiveness, simplicity and practicality of the proposed control scheme.     

一类具有未知死区MIMO系统的自适应模糊控制

针对一类具有未知死区并具有下三角函数控制增益矩阵的不确定MIMO非线性系统, 根据滑模控制原理, 并利用Nussbaum函数的性质, 提出了一种自适应模糊控制器的设计方案. 该方案取消了函数控制增益符号已知和死区模型参数上界、下界已知的条件. 通过引入积分型李亚普诺夫函数及最优逼近误差与死区扰动上界的自适应补偿项，证明了闭环系统是稳定的，跟踪误差收敛到零. 仿真结果表明了该方法的有效性.     

Robust adaptive tracking control for a class of switched time-delay systems with application of vehicle roll dynamic control

The problems of stability and robust tracking control for a class of switched nonlinear systems with uncertain input and state delays are investigated in this study. In the presence of unknown functions and external disturbances, an adaptive fuzzy technique based on nonlinear disturbance observer is used to counteract the effects of external disturbances and approximate unknown functions. For this purpose, it is first assumed that a common Lyapunov function exists for the switched system, and then a new common Lyapunov–Krasovskii functional is built using the terms of the hypothetical common Lyapunov function. By employing this new function, the delay-dependent input-to-state stability (ISS) under an arbitrary switching signal is provided. The robust tracking control problem for this system is investigated next. Finally, to assure ISS and robust tracking performance, an adaptive control law is developed that ensures conditions of the aforementioned hypothetical common Lyapunov function. In addition, to demonstrate the efficiency of the proposed strategy, the aforesaid method is applied to a vehicle roll dynamic as well as a mass-spring system.     

Dynamic structure adaptive neural fuzzy control for MIMO uncertain nonlinear systems

This paper proposes a novel dynamic structure neural fuzzy network (DSNFN) to address the adaptive tracking problems of multiple-input-multiple-output (MIMO) uncertain nonlinear systems. The proposed control scheme uses a four-layer neural fuzzy network (NFN) to estimate system uncertainties online. The main feature of this DSNFN is that it can either increase or decrease the number of fuzzy rules over time based on tracking errors. Projection-type adaptation laws for the network parameters are derived from the Lyapunov synthesis approach to ensure network convergence and stable control. A hybrid control scheme that combines the sliding-mode control and the adaptive bound estimation control with different weights improves system performance by suppressing the influence of external disturbances and approximation errors. As the employment of the DSNFN, high-quality tracking performance could be achieved in the system. Furthermore, the trained network avoids the problems of overfitting and underfitting. Simulations performed on a two-link robot manipulator demonstrate the effectiveness of the proposed control scheme.     

An adaptive neuro-fuzzy tracking control for multi-input nonlinear dynamic systems

An adaptive neuro-fuzzy control design is suggested in this paper, for tracking of nonlinear affine in the control dynamic systems with unknown nonlinearities. The plant is described by a Takagi–Sugeno (T–S) fuzzy model, where the local submodels are realized through nonlinear dynamical input–output mappings. Our approach relies upon the effective approximation of certain terms that involve the derivative of the Lyapunov function and the unknown system nonlinearities. The above task is achieved locally, using linear in the weights neural networks. A novel resetting scheme is proposed that assures validity of the control input. Stability analysis provides the control law and the adaptation rules for the network weights, assuring uniform ultimate boundedness of the tracking and the signals appearing in the closed-loop configuration. Illustrative simulations highlight the approach.     

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.     

Fuzzy adaptive output feedback control for a class of switched non-triangular structure nonlinear systems with time-varying delays

This paper investigates an adaptive fuzzy output feedback control design problem for switched nonlinear system in non-triangular structure form. The discussed system contains unknown nonlinear dynamics, unmeasured states and unknown time-varying delays under a batch of switching signals. Fuzzy logic systems are utilised to learn unknown nonlinear dynamics and construct a fuzzy switched nonlinear observer. By combining the property of fuzzy basis function with Lyapunov–Krasovskii functional and the command filter, a novel observer-based fuzzy adaptive backstepping schematic design algorithm is presented. Furthermore, the stability of the closed-loop control system is proved via Lyapunov stability theory and average dwell time method. The simulation results are presented to verify the validity of the proposed control scheme.     

基于终端滑模机器人模糊自适应路径跟踪控制

对质心位置未知的移动机器人系统设计了基于快速终端滑模的模糊自适应路径跟踪控制方法。该方法采用模糊逻辑系统逼近控制器中的未知函数,基于李亚普诺夫稳定性分析方法对未知参数设计自适应律,并设计鲁棒控制器来补偿逼近误差。该方法不但可以保证闭环系统中的所有信号有界,而且可使跟踪误差在有限时间内收敛到原点的小邻域内。仿真结果验证了方法的有效性。     

基于自适应神经网络的不确定非线性系统的模糊跟踪控制

提出了一种基于模糊模型和自适应神经网络的跟踪控制方法.在系统具有未知不确定非线性特性的情况下,首先利用T＿S模糊模型对系统的已知特性进行近似建模,对基于模糊模型的模糊H∞跟踪控制律进行输出跟踪控制.并在此基础上,进一步采用RBF神经网络完全自适应控制,通过在线自适应调整RBF神经网络的权重、函数中心和宽度,从而有效地消除系统的未知不确定性和模糊建模误差的影响,保证了非线性闭环系统的稳定性和系统的H∞跟踪性能,而不要求系统的不确定项和模糊建模误差满足任何匹配条件或约束.最后,将所提出的方法应用到一非线性混沌系统,仿真结果表明了所提出的方案不仅能够有效地稳定该混沌系统,而且能使系统输出跟踪期望输出.     

带有饱和的电机伺服系统非奇异终端滑模funnel控制

本文提出一种非奇异终端滑模funnel控制(NTSMFC)方法, 实现带有饱和输入电机伺服系统的指定性能跟踪控制. 根据中值定理, 非光滑饱和函数转化为放射形式, 并且应用一个简单的神经网络进行逼近和补偿. 为保证跟踪误差被限制在指定的界限内, 同时为避免构建复杂的barrier李雅普诺夫函数或逆函数, 本文采用一个新的限制变量. 然后, 构建非奇异终端滑模funnel控制器保证电机伺服系统的指定跟踪性能. 该方法无需事先已知输入饱和函数的界限等先验知识, 且基于李雅普诺夫函数设计可以保证位置跟踪误差的收敛性, 最后给出仿真对比实例证明了该方法的有效性.     

基于修正闭环子空间辨识--分段线性结构的 环管式丙烯聚合反应过程非线性模型预测控

本文提出一种非奇异终端滑模funnel控制(NTSMFC)方法, 实现带有饱和输入电机伺服系统的指定性能跟踪控制. 根据中值定理, 非光滑饱和函数转化为放射形式, 并且应用一个简单的神经网络进行逼近和补偿. 为保证跟踪误差被限制在指定的界限内, 同时为避免构建复杂的barrier李雅普诺夫函数或逆函数, 本文采用一个新的限制变量. 然后, 构建非奇异终端滑模funnel控制器保证电机伺服系统的指定跟踪性能. 该方法无需事先已知输入饱和函数的界限等先验知识, 且基于李雅普诺夫函数设计可以保证位置跟踪误差的收敛性, 最后给出仿真对比实例证明了该方法的有效性.     

A design for a class of nonlinear systems with delay time using fuzzy logic

 The goal of this paper is to design a controller for a class of nonlinear systems with delay time using fuzzy logic. The control scheme considered in this paper integrates a fuzzy component and a sliding control component. In the former, the fuzzy system can be considered as a universal approximator to approximate the unknown functions in plant. In the latter, a variable structure control with a sector guarantees the global stability of the closed-loop system when a variable, involving tracking error, travels outside of the sector. The adaptive laws to adjust the parameters in the system are developed based on the Lyapunov synthesis approach. It is shown that the proposed adaptive controller guarantees tracking error, between the outputs of the considered system and desired␣values, to be asymptotical in decay.