Robust adaptive fuzzy control scheme for nonlinear system with uncertainty

In this paper, a robust adaptive fuzzy control scheme for a class of nonlinear system with uncertainty is proposed. First, using prior knowledge about the plant we obtain a fuzzy model, which is called the generalized fuzzy hyperbolic model (GFHM). Secondly, for the case that the states of the system are not available an observer is designed and a robust adaptive fuzzy output feedback control scheme is developed. The overall control system guarantees that the tracking error converges to a small neighborhood of origin and that all signals involved are uniformly bounded. The main advantages of the proposed control scheme are that the human knowledge about the plant under control can be used to design the controller and only one parameter in the adaptive mechanism needs to be on-line adjusted.     

Robust adaptive fuzzy control scheme for nonlinear system with uncertainty

In this paper, a robust adaptive fuzzy control scheme for a class of nonlinear system with uncertainty is proposed. First, using prior knowledge about the plant we obtain a fuzzy model, which is called the generalized fuzzy hyperbolic model （GFHM）. Secondly, for the case that the states of the system are not available an observer is designed and a robust adaptive fuzzy output feedback control scheme is developed. The overall control system guarantees that the tracking error converges to a small neighborhood of origin and that all signals involved are uniformly bounded. The main advantages of the proposed control scheme are that the human knowledge about the plant under control can be used to design the controller and only one parameter in the adaptive mechanism needs to be on-line adjusted.     

一类非线性不确定系统的神经网络控制

针对一类非线性不确定系统,提出了一种自适 应神经网络控制方案．被控系统是部分已知的,其中系统已知的动态特性被用来设计保证标 称模型稳定的反馈控制器,而基于神经网络的动态补偿器则用于补偿系统的非线性不确定性 ,从而可以保证系统输出跟踪误差渐近收敛于0．     

Adaptive fuzzy learning control for a class of nonlinear dynamic systems

This paper presents an adaptive iterative learning control scheme that is applicable to a class of nonlinear systems. The control scheme guarantees system stability and boundedness by using the feedback controller coupled with the fuzzy compensator and achieves precise tracking by using the iterative learning rules. In the feedback plus fuzzy compensator unit, the feedback control part stabilizes the overall closed‐loop system and keeps its error bounded, and the fuzzy compensator estimates and compensates for the nonlinear part of the system, thereby keeping the feedback gains reasonably low in the feedback controller. The fuzzy compensator is designed by applying the fuzzy approximation technique to the uncertain nonlinear term to be compensated. In the iterative learning controller, a simple learning control rule is used to achieve precise tracking of the reference signal and a parameter learning algorithm is used to update the parameters in the fuzzy compensator so as to identify the uncertain nonlinearity as much as possible. © 2000 John Wiley & Sons, Inc.     

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.     

Adaptive fuzzy sliding mode controller for a class of SISO nonlinear time-delay systems

In this paper, we propose an adaptive fuzzy controller for a class of nonlinear SISO time-delay systems. The plant model structure is represented by a Takagi–Sugeno (T–S) type fuzzy system. The T–S fuzzy model parameters are adjusted online. The proposed algorithm utilizes the sliding surface to adjust online the parameters of T–S fuzzy model. The controller is based on adjustable T–S fuzzy parameters model and sliding mode theory. The stability analysis of the closed-loop system is based on the Lyapunov approach. The plant state follows asymptotically any bounded reference signal. Two examples have been used to check performances of the proposed fuzzy adaptive 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.     

一类多变量非线性动态系统的鲁棒自适应模糊控制

对一类非线性多变量未知动态系统,提出了一种自适应模糊控制策略.策略中采用IF-THEN推理规则来构造模糊逻辑系统,实现对系统中未知函数的估计,在建模误差为零的条件下设计状态反馈控制器及参数的自适应律.分析了当存在建模误差时,闭环系统的稳定性和鲁棒性.     

Stable multi-input multi-output adaptive fuzzy/neural control

In this letter, stable direct and indirect adaptive controllers are presented that use Takagi-Sugeno (T-S) fuzzy systems (1985), conventional fuzzy systems, or a class of neural networks to provide asymptotic tracking of a reference signal vector for a class of continuous time multi-input multi-output (MIMO) square nonlinear plants with poorly understood dynamics. The direct adaptive scheme allows for the inclusion of a priori knowledge about the control input in terms of exact mathematical equations or linguistics, while the indirect adaptive controller permits the explicit use of equations to represent portions of the plant dynamics. We prove that with or without such knowledge the adaptive schemes can “learn” how to control the plant, provide for bounded internal signals, and achieve asymptotically stable tracking of the reference inputs. We do not impose any initialization conditions on the controllers and guarantee convergence of the tracking error to zero     

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.     

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     

Indirect adaptive fuzzy and impulsive control of nonlinear systems

The problem of indirect adaptive fuzzy and impulsive control for a class of nonlinear systems is investigated. Based on the approximation capability of fuzzy systems, a novel adaptive fuzzy and impulsive control strategy with supervisory controller is developed. With the help of a supervisory controller, global stability of the resulting closed-loop system is established in the sense that all signals involved are uniformly bounded. Furthermore, the adaptive compensation term of the upper bound function of the sum of residual and approximation error is adopted to reduce the effects of modeling error. By the generalized Barbalat's lemma, the tracking error between the output of the system and the reference signal is proved to be convergent to zero asymptotically. Simulation results illustrate the effectiveness of the proposed approach.     

Output feedback preview control for polytopic uncertain discrete‐time systems with time‐varying delay

This paper considers the preview tracking control problem of polytopic uncertain discrete‐time systems with a time‐varying delay subject to a previewable reference signal. First, a model transformation is employed and a discrete‐time system with a time‐invariant delay and an external disturbance is obtained. The difference operator method can be extended to derive an augmented error system that includes future information on the reference signal. Then, a previewable reference signal is fully utilized through reformulation of the output equation while considering the output feedback. Based on the small gain theorem, a static output feedback controller with preview actions is designed such that the output can asymptotically track the reference signal. Finally, numerical simulation examples also illustrate the superiority of the desired preview controller for the uncertain system in the paper.     

Stable adaptive control using fuzzy systems and neural networks

Stable direct and indirect adaptive controllers are presented, which use Takagi-Sugeno fuzzy systems, conventional fuzzy systems, or a class of neural networks to provide asymptotic tracking of a reference signal for a class of continuous-time nonlinear plants with poorly understood dynamics. The indirect adaptive scheme allows for the inclusion of a priori knowledge about the plant dynamics in terms of exact mathematical equations or linguistics while the direct adaptive scheme allows for the incorporation of such a priori knowledge in specifying the controller. We prove that with or without such knowledge both adaptive schemes can “learn” how to control the plant, provide for bounded internal signals, and achieve asymptotically stable tracking of a reference input. In addition, for the direct adaptive scheme a technique is presented in which linguistic knowledge of the inverse dynamics of the plant may be used to accelerate adaptation. The performance of the indirect and direct adaptive schemes is demonstrated through the longitudinal control of an automobile within an automated lane     

Stable adaptive fuzzy control of nonlinear systems using small-gain theorem and LMI approach

A new design scheme of stable adaptive fuzzy control for a class of nonlinear systems is proposed in this paper. The T-S fuzzy model is employed to represent the systems. First, the concept of the so-called parallel distributed compensation (PDC) and linear matrix inequality (LMI) approach are employed to design the state feedback controller without considering the error caused by fuzzy modeling. Sufficient conditions with respect to decay rate α are derived in the sense of Lyapunov asymptotic stability. Finally, the error caused by fuzzy modeling is considered and the input-tostate stable (ISS) method is used to design the adaptive compensation term to reduce the effect of the modeling error. By the small-gain theorem, the resulting closed-loop system is proved to be input-to-state stable. Theoretical analysis verifies that the state converges to zero and all signals of the closed-loop systems are bounded. The effectiveness of the proposed controller design methodology is demonstrated through numerical simulation on the chaotic Henon system.     

Intelligent process control using neural fuzzy techniques

In this paper, we combine the advantages of fuzzy logic and neural network techniques to develop an intelligent control system for processes having complex, unknown and uncertain dynamics. In the proposed scheme, a neural fuzzy controller (NFC), which is constructed by an equivalent four-layer connectionist network, is adopted as the process feedback controller. With a derived learning algorithm, the NFC is able to learn to control a process adaptively by updating the fuzzy rules and the membership functions. To identify the input–output dynamic behavior of an unknown plant and therefore give a reference signal to the NFC, a shape-tunable neural network with an error back-propagation algorithm is implemented. As a case study, we implemented the proposed algorithm to the direct adaptive control of an open-loop unstable nonlinear CSTR. Some important issues were studied extensively. Simulation comparison with a conventional static fuzzy controller was also performed. Extensive simulation results show that the proposed scheme appears to be a promising approach to the intelligent control of complex and unknown plants, which is directly operational and does not require any a priori system information.     

非线性动态突变系统的多模型自适应执行器故障补偿设计

本文针对因多重不确定执行器故障而引起系统动态突变的非线性系统, 设计了一种基于多模型切换的自适应执行器故障补偿控制策略, 以提高系统应对动态突变的能力, 同时实现不确定执行器故障的快速精确补偿. 针对执行器故障模式的不确定性问题, 采用基于多模型的参数估计方法, 设计了自适应控制器组; 基于最优性能指标函数, 提出了一种控制切换机制, 以选择最佳的自适应控制器作为当前的控制器, 从而实现期望的故障补偿控制. 所设计的多模型自适应控制策略, 可以保证所有闭环系统信号有界, 且在出现有限数量的不确定性执行器故障情况下, 系统输出渐近跟踪所选择的参考系统输出; 同时, 当系统中出现持续间歇性执行器故障时, 此方法可以保证系统的输出跟踪误差是平均小的. 最后, 本文基于飞行器动力学模型, 进行仿真研究, 验证了所设计的自适应故障补偿策略的有效性.     

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.     

Backstepping adaptive fuzzy control of uncertain nonlinear systems against actuator faults

A class of unknown nonlinear systems subject to uncertain actuator faults and external disturbances will be studied in this paper with the help of fuzzy approximation theory. Using backstepping technique, a novel adaptive fuzzy control approach is proposed to accommodate the uncertain actuator faults during operation and deal with the external disturbances though the systems cannot be linearized by feedback. The considered faults are modeled as both loss of effectiveness and lock-in-place （stuck at some unknown place）. It is proved that the proposed control scheme can guarantee all signals of the closed-loop system to be semi-globally uniformly ultimately bounded and the tracking error between the system output and the reference signal converge to a small neighborhood of zero, though the nonlinear functions of the controlled system as well as the actuator faults and the external disturbances are all unknown. Simulation results demonstrate the effectiveness of the control approach.