The adaptive control of nonlinear systems using the Sugeno-type offuzzy logic

An adaptive fuzzy controller is synthesized from a collection of fuzzy IF-THEN rules. The parameters of the membership functions characterizing the linguistic terms in the fuzzy IF-THEN rules are changed according to some adaptive laws for the purpose of controlling a plant to track a reference trajectory. In the paper, a direct adaptive fuzzy control design method is developed for the general higher order nonlinear continuous systems. We use the Sugeno-type of the fuzzy logic system to approximate the controller. It is proved that the closed-loop system using this adaptive fuzzy controller is globally stable in the sense that all signals involved are bounded. Finally, we apply the method of direct adaptive fuzzy controllers to control an unstable system     

Stable adaptive fuzzy control of nonlinear systems

A direct adaptive fuzzy controller that does not require an accurate mathematical model of the system under control, is capable of incorporating fuzzy if-then control rules directly into the controllers, and guarantees the global stability of the resulting closed-loop system in the sense that all signals involved are uniformly bounded is developed. The specific formula for the bounds is provided, so that controller designers can determine the bounds based on their requirements. The direct adaptive fuzzy controller is used to regulate an unstable system to the origin and to control the Duffing chaotic system to track a trajectory. The simulation results show that the controller worked without using any fuzzy control rules, and that after fuzzy control rules were incorporated the adaptation speed became much faster. It is shown explicitly how the supervisory control forces the state to remain within the constraint set and how the adaptive fuzzy controller learns to regain control     

Fuzzy-identification-based adaptive backstepping control using a self-organizing fuzzy system

In this paper, a fuzzy-identification-based adaptive backstepping control (FABC) scheme is proposed. The FABC system is composed of a backstepping controller and a robust controller. The backstepping controller, which uses a self-organizing fuzzy system (SFS) with the structure and parameter learning phases to on-line estimate the controlled system dynamics, is the principal controller, and the robust controller is designed to dispel the effect of approximation error introduced by the SFS. The developed SFS automatically generates and prunes the fuzzy rules by the proposed structure adaptation algorithm and the parameters of the fuzzy rules and membership functions tunes on-line in the Lyapunov sense. Thus, the overall closed-loop FABC system can guarantee that the tracking error and parameter estimation error are uniformly ultimately bounded; and the tracking error converges to a desired small neighborhood around zero. Finally, the proposed FABC system is applied to a chaotic dynamic system to show its effectiveness. The simulation results verify that the proposed FABC system can achieve favorable tracking performance even with unknown controlled system dynamics.     

一类动态不确定系统的自适应模糊控制

针对一类不确定性系统, 用back-stepping设计方法设计了一种新的模糊控制器, 并在所有信号一致有界的意义上证明了系统的稳定性, 仿真结果表明本文所设计的控制器能达到预定的目的.     

Adaptive hybrid intelligent control for uncertain nonlinear dynamical systems

A new hybrid direct/indirect adaptive fuzzy neural network (FNN) controller with a state observer and supervisory controller for a class of uncertain nonlinear dynamic systems is developed in this paper. The hybrid adaptive FNN controller, the free parameters of which can be tuned on-line by an observer-based output feedback control law and adaptive law, is a combination of direct and indirect adaptive FNN controllers. A weighting factor, which can be adjusted by the tradeoff between plant knowledge and control knowledge, is adopted to sum together the control efforts from indirect adaptive FNN controller and direct adaptive FNN controller. Furthermore, a supervisory controller is appended into the FNN controller to force the state to be within the constraint set. Therefore, if the FNN controller cannot maintain the stability, the supervisory controller starts working to guarantee stability. On the other hand, if the FNN controller works well, the supervisory controller will be deactivated. The overall adaptive scheme guarantees the global stability of the resulting closed-loop system in the sense that all signals involved are uniformly bounded. Two nonlinear systems, namely, inverted pendulum system and Chua's (1989) chaotic circuit, are fully illustrated to track sinusoidal signals. The resulting hybrid direct/indirect FNN control systems show better performances, i.e., tracking error and control effort can be made smaller and it is more flexible during the design process.     

HGO-based decentralised indirect adaptive fuzzy control for a class of large-scale nonlinear systems

In this article, a novel high gain observer (HGO)-based decentralised indirect adaptive fuzzy controller is developed for a class of uncertain affine large-scale nonlinear systems. By the combination of fuzzy logic systems and an HGO, the state variables are not required to be measurable. The proposed feedback and adaptation mechanisms guarantee that each subsystem is able to adaptively compensate for interconnections and disturbances with unknown bounds. It is ascertained using a singular perturbation method that all the signals of the closed-loop large-scale system stand uniformly ultimately bounded and the tracking errors converge to tunable neighbourhoods of the origin. Simulation results of correlated double inverted pendulums substantiate the effectiveness of the proposed controller.     

基于线性T-S模糊系统的自适应系统的设计和稳定性分析

提出了一种新型的模糊自适应控制器.其中系统的未知函数由线性T-S模糊系统估计, 模糊规则的后件是线性可调的.因线性T-S模糊系统较之Mamdani模糊系统具有更好的估计性 能,我们可以获得更小的跟踪误差.由于采用李亚普诺夫合成方法来设计控制器,整个闭环系统 全局稳定,所有的信号有界.对倒立摆的仿真验证了这一点.     

Adaptive Fuzzy Output Tracking Control of MIMO Nonlinear Uncertain Systems

In this paper, the adaptive fuzzy tracking control problem is discussed for a class of uncertain multiple-input-multiple-output (MIMO) nonlinear systems with the block-triangular structure. The fuzzy logic systems are used to approximate the unknown nonlinear functions. By using the backstepping technique, the adaptive fuzzy tracking control design scheme is developed, which has minimal learning parameterizations. The adaptive fuzzy tracking controllers guarantee that the outputs of systems converge to a small neighborhood of the reference signals and all the signals in the closed-loop system are semiglobally uniformly ultimately bounded. Two examples are used to show the effectiveness of the approach     

Adaptive fuzzy control with compressors and limiters for a class of uncertain nonlinear systems

This paper proposes a novel adaptive fuzzy control design for a class of nonlinear uncertain systems. The definition of compressor and limiter with adjustable parameters is introduced at beginning, and then updated laws of parameters of the compressor and estimate values of fuzzy approximation accuracies are utilized to synthesize stable adaptive controllers. The most advantage of designing adaptive fuzzy controller is neglectful of the logic structure of fuzzy logic systems, which make designer focus on parameters of the compressor, limiter and fuzzy approximation accuracies. This adaptive fuzzy control method can not only reduce the number of on-line updated parameters but also guarantee states of the closed-loop system to be uniformly ultimately bounded (UUB). Simulation results demonstrate the effectiveness of the control scheme in this paper.     

一类分布式系统的自适应跟踪和扰动抑制

研究直接自适应状态反馈控制策略解决一类有故障和摄动关联链接的分布式大系统渐进跟踪和扰动抑制问题. 根据特殊的分布式结构, 在所有关联故障因子, 关联通道摄动和子系统外部干扰的上界都未知下, 提出自适应率在线升级控制器参数. 基于自适应策略信息, 构造一类分布式状态反馈控制器自动补偿故障和摄动影响, 同时抑制外部扰动. 在关联通道有故障摄动和外部扰动情况下, 所提出的自适应鲁棒跟踪控制器可以保证所得自适应闭环大系统稳定, 及每个子系统渐进输出跟踪所对应参考信号. 最后由一个仿真例子评估所提技术的有效性.     

Robust decentralized direct adaptive output feedback fuzzy control for a class of large-sale nonaffine nonlinear systems

In the previous work of Huang et al., a decentralized direct adaptive fuzzy H_∞ tracking controller of large-scale nonaffine nonlinear systems is obtained predicated upon the assumption that the mismatching error dynamics stay squared integrable. In this note, we focus in the absence of the conservative assumption upon developing a robust decentralized direct adaptive output feedback fuzzy controller. By combination of a state observer, a fuzzy inference system and robust control technique, the previous controller design is modified and no a priori knowledge of bounds on lumped uncertainties is required. All the signals of the closed-loop large-scale system are proved to be uniformly ultimately bounded. The effectiveness of the developed scheme is demonstrated through the simulation results of interconnected inverted pendulums.     

变论域自适应模糊控制及其在Chua's混沌电路中的应用

本文研究输出反馈自适应变论域模糊控制方法.变论域模糊控制通过自适应调节伸缩因子,生成大量规则,提高了系统的控制精度.由于状态的不完全可测,本文首先通过构造状态观测器实现输出反馈控制.然后,为了抑制外部扰动和参数变化,通过监督控制将系统的状态约束在给定的范围之内,从而提高了控制器的精度和鲁棒性.进而利用Lyapunov函数证明了观测器-控制器系统的稳定性;在所有状态一致有界的前提下,整个自适应控制算法保证闭环系统的稳定性.最后将所提算法应用于Chua s混沌电路,仿真结果证明了控制方法的有效性.     

Synchronization of uncertain chaotic systems based on adaptive type-2 fuzzy sliding mode control

A novel direct adaptive interval type-2 fuzzy neural network (FNN) controller in which linguistic fuzzy control rules can be directly incorporated into the controller is developed to synchronize chaotic systems with training data corrupted by noise or rule uncertainties involving external disturbances, in this paper. By incorporating direct adaptive interval type-2 FNN control scheme and sliding mode approach, two non-identical chaotic systems can be synchronized based on Lyapunov stability criterion. Moreover, the chattering phenomena of the control efforts can be reduced and the external disturbance on the synchronization error can be attenuated. The stability of the proposed overall adaptive control scheme will be guaranteed in the sense that all the states and signals are uniformly bounded. From the simulation example, to synchronize two non-identical Chua’s chaotic circuits, it has been shown that type-2 FNN controllers have the potential to overcome the limitations of tpe-1 FNN controllers when training data is corrupted by high levels of uncertainty.     

Distributed adaptive robust tracking and model matching control with actuator faults and interconnection failures

In this paper, direct adaptive-state feedback control schemes are developed to solve the robust tracking and model matching control problem for a class of distributed large scale systems with actuator faults, faulty and perturbed interconnection links, and external disturbances. The adaptation laws are proposed to update the controller parameters on-line when all the eventual faults, the upper bounds of perturbations and disturbances are assumed to be unknown. Then a class of distributed state feedback controllers is constructed to automatically compensate the fault, perturbation and disturbance effects based on the information from adaptive schemes. The proposed distributed adaptive tracking controller can ensure that the resulting adaptive closed-loop large-scale system is stable and the tracking error decreases asymptotically to zero in the presence of uncertain faults of actuators and interconnections, perturbations in interconnection channels, and disturbances. The proposed adaptive design technique is finally evaluated in the light of a simulation example.     

Adaptive fuzzy observer backstepping control for a class of uncertain nonlinear systems with unknown time-delay

In this paper, a new adaptive fuzzy backstepping control approach is developed for a class of nonlinear systems with unknown time-delay and unmeasured states. Using fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy state observer is designed for estimating the unmeasured states. On the basis of the state observer and applying the backstepping technique, an adaptive fuzzy observer control approach is developed. The main features of the proposed adaptive fuzzy control approach not only guarantees that all the signals of the closed-loop system are semiglobally uniformly ultimately bounded, but also contain less adaptation parameters to be updated on-line. Finally, simulation results are provided to show the effectiveness of the proposed approach.     

Distributed adaptive output feedback tracking control for a class of uncertain nonlinear multi-agent systems

This paper addresses the distributed output feedback tracking control problem for multi-agent systems with higher order nonlinear non-strict-feedback dynamics and directed communication graphs. The existing works usually design a distributed consensus controller using all the states of each agent, which are often immeasurable, especially in nonlinear systems. In this paper, based only on the relative output between itself and its neighbours, a distributed adaptive consensus control law is proposed for each agent using the backstepping technique and approximation technique of Fourier series (FS) to solve the output feedback tracking control problem of multi-agent systems. The FS structure is taken not only for tracking the unknown nonlinear dynamics but also the unknown derivatives of virtual controllers in the controller design procedure, which can therefore prevent virtual controllers from containing uncertain terms. The projection algorithm is applied to ensure that the estimated parameters remain in some known bounded sets. Lyapunov stability analysis shows that the proposed control law can guarantee that the output of each agent synchronises to the leader with bounded residual errors and that all the signals in the closed-loop system are uniformly ultimately bounded. Simulation results have verified the performance and feasibility of the proposed distributed adaptive control strategy.     

Fuzzy adaptive filters, with application to nonlinear channelequalization

Two fuzzy adaptive filters are developed: one uses a recursive-least-squares (RLS) adaptation algorithm, and the other uses a least-mean-square (LMS) adaptation algorithm. The RLS fuzzy adaptive filter is constructed through the following four steps: (1) define fuzzy sets in the filter input space Rn whose membership functions cover U; (2) construct a set of fuzzy IF-THEN rules which either come from human experts or are determined during the adaptation procedure by matching input-output data pairs; (3) construct a filter based on the set of rules; and (4) update the free parameters of the filter using the RLS algorithm. The design procedure for the LMS fuzzy adaptive filter is similar. The most important advantage of the fuzzy adaptive filters is that linguistic information (in the form of fuzzy IF-THEN rules) and numerical information (in the form of input-output pairs) can be combined in the filters in a uniform fashion. The filters are applied to nonlinear communication channel equalization problems     

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.     

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.