Adaptive Fuzzy Backstepping Tracking Control for Flexible Robotic Manipulator

In this paper, an adaptive fuzzy state feedback control method is proposed for the single-link robotic manipulator system. The considered system contains unknown nonlinear function and actuator saturation. Fuzzy logic systems (FLSs) and a smooth function are used to approximate the unknown nonlinearities and the actuator saturation, respectively. By combining the command-filter technique with the backstepping design algorithm, a novel adaptive fuzzy tracking backstepping control method is developed. It is proved that the adaptive fuzzy control scheme can guarantee that all the variables in the closed-loop system are bounded, and the system output can track the given reference signal as close as possible. Simulation results are provided to illustrate the effectiveness of the proposed approach.      

Low‐complexity adaptive tracking control of MIMO nonlinear systems with unknown control directions

This paper is concerned with the tracking control problem for a class of multiple‐input–multiple‐output systems with unmatched disturbances and the unknown additive and multiplicative nonlinearities. The objective is to provide a low‐complexity control solution in the sense that (i) approximating structures are not involved, despite unknown nonlinearities and (ii) iterative calculations of command derivatives are avoided in the backstepping design. A robust adaptive control strategy is proposed to fulfill the task. In the control design, a new‐type adaptive law is first developed to update Nussbaum gains to handle control direction uncertainties, while ensuring Nussbaum gains bounded. Then, the potential robustness of error constraint techniques is exploited to counteract the effects of unknown nonlinearities and disturbances and achieve predefined transient and steady‐state tracking performance. Finally, simulation results are given to illustrate the above theoretical findings.     

Fuzzy adaptive robust backstepping stabilization for SISO nonlinear systems with unknown virtual control direction

In this paper, a direct fuzzy adaptive robust control approach is proposed for a class of SISO nonlinear systems with completely unknown virtual control directions, unknown nonlinearities, unmodeled dynamics and dynamic disturbances. In the backstepping recursive design, fuzzy logic systems are employed to approximate the combined nonlinear uncertainties, a dynamic signal and Nussbaum gain technique are introduced into the control scheme to dominate the dynamic uncertainties and solve the unknown signs of virtual control directions, respectively. It is proved that the proposed robust fuzzy adaptive scheme can guarantee the all signals in the closed-loop system are semi-globally uniformly ultimately bounded. The effectiveness of the proposed approach is illustrated via three examples.     

不确定非线性多智能体系统的分布式模糊自适应镇定控制

针对一类具有未知非线性和未知参数摄动的非线性多智能体系统, 提出一种分布式模糊自适应镇定控制方法. 基于邻接智能体信息和部分智能体的自身信息, 分别设计静态耦合和动态耦合的分布式模糊自适应控制律. 基于Lyapunov 稳定性理论, 证明了所提出的控制器能使得系统状态最终稳定于原点的邻域内. 仿真实例验证了所提出方法的有效性.

     

Cooperative Adaptive Fuzzy Output Feedback Control for Synchronization of Nonlinear Multi‐Agent Systems in the Presence of Input Saturation

This paper considers the leader‐following synchronization problem of nonlinear multi‐agent systems with unmeasurable states in the presence of input saturation. Each follower is governed by a class of strict‐feedback systems with unknown nonlinearities and the information of the leader can be accessed by only a small fraction of followers. An auxiliary system is introduced and its states are used to design the cooperative controllers for counteracting the effect of input saturation. By using fuzzy logic systems to approximate the unknown nonlinearities, local adaptive fuzzy observers are designed to estimate the unmeasurable states. Dynamic surface control (DSC) is employed to design distributed adaptive fuzzy output feedback controllers. The developed controllers guarantee that the outputs of all followers synchronize to that of the leader under directed communication graphs. Based on Lyapunov stability theory, it is proved that all signals in the closed‐loop systems are semiglobally uniformly ultimately bounded (SGUUB), and the tracking error converges to a small neighborhood of the origin. An example is provided to show the effectiveness of the proposed control approach.     

Observer-based adaptive fuzzy tracking control for a class of MIMO nonlinear systems with unknown dead zones and time-varying delays

The adaptive tracking control strategy is investigated for a class of multi-input and multi-output pure-feedback nonlinear delayed systems with unknown dead-zone inputs. This problem is challenging due to the existence of unknown dead zones, time-varying delays and unavoidable state variables. By constructing fuzzy approximators and state observers, the difficulties from unknown nonlinearities and unavailable state variables are surmounted, respectively. Lyapunov–Krasovskii functions are introduced to deal with the time-varying delays. The adaptive controllers are designed by a backstepping method and adaptive technique so that the closed-loop systems remain stable and the target signals can be tracked within a small error as well. At last, two examples are provided to show the effectiveness of the proposed scheme.     

An architecture for adaptive fuzzy control in industrial environments

The paper presents an architecture for adaptive fuzzy control of industrial systems. Both conventional and adaptive fuzzy control can be designed. The control methodology can integrate a priori knowledge about the control and/or about the plant, with on-line control adaptation mechanisms to cope with time-varying and/or uncertain plant parameters. The paper presents the fuzzy control software architecture that can be integrated in industrial processing and communication structures. It includes four distinct modules: a mathematical fuzzy library, a graphical user interface (GUI), fuzzy controller, and industrial communication. Three types of adaptive fuzzy control methods have been studied, and compared: (1) direct adaptive, (2) indirect adaptive, and (3) combined direct/indirect adaptive. An experimental benchmark composed of two mechanically coupled electrical DC motors has been employed to study the performance of the presented control architectures. The first motor acts as an actuator, while the second motor is used to generate nonlinearities and/or time-varying load. Results indicate that all tested controllers have good performance in overcoming changes of DC motor load.     

Adaptive fuzzy decentralised fault-tolerant control for nonlinear large-scale systems with actuator failures and unmodelled dynamics

This paper discusses the adaptive fuzzy decentralised fault-tolerant control (FTC) problem for a class of nonlinear large-scale systems in strict-feedback form. The systems under study contain the unknown nonlinearities, unmodelled dynamics, actuator faults and without the direct measurements of state variables. With the help of fuzzy logic systems identifying the unknown functions and a fuzzy adaptive observer is designed to estimate the unmeasured states. By using the backstepping design technique and the dynamic surface control approach and combining with the changing supply function technique, a fuzzy adaptive FTC scheme is developed. The main features of the proposed control approach are that it can guarantee the closed-loop system to be input–to-state practically stable, and also has the robustness to the unmodelled dynamics. Moreover, it can overcome the so-called problem of ‘explosion of complexity’ existing in the previous literature. Finally, simulation studies are provided to illustrate the effectiveness of the proposed approach.     

Adaptive stabilisation of networked control systems tolerant to unknown actuator failures

In this article, adaptive state feedback stabilising controllers for networked adaptive control systems with unknown actuator failures are developed. The problems of networked control systems (NCSs) such as transmission delays and data-packets dropout, induced by the insertion of data networks in the feedback adaptive control loops are also considered. The novelty of this article consists in the combination of different aspects in NCSs: state tracking control of systems with unknown parameters, unknown actuator failures, network-induced delays and data-packets dropout. Normalised adaptive laws are designed for updating the controller parameters. Sufficient conditions for Lyapunov stability are derived in the case of uncertainty due to actuator failures, delays and data-packets dropout. Simulation results are given to illustrate the effectiveness of our design approach.     

Improved prescribed performance control for nonlinear systems with unknown control direction and input dead-zone

In view of the input dead-zone, unknown control direction and difficulty in satisfying the prescribed performance that suffered in practical systems, an improved prescribed performance-based adaptive control scheme is stressed for uncertain nonlinear systems in this paper. Firstly, by adopting a characteristic function, the input dead-zone is linearized to a model with bounded perturbation. To settle the “computation complexity” issue, an adaptive controller is built via command filter design method, where the fuzzy logic systems are introduced to approximate the unknown nonlinearities. Meanwhile, the Nussbaum function is brought in controller design to counter the hardship of unknown control direction. Besides, the tracking error can be restricted in the prescribed boundary in finite time with the improved performance function. The presented control approach can not only ensure the finite-time convergence property of tracking error and the boundedness of all signals in the closed-loop system, but also easily implement in engineering. Finally, the simulation examples confirm the validity of the designed control scheme.     

Adaptive quantised fault-tolerant tracking control of uncertain nonlinear systems with unknown control direction and the prescribed accuracy

In this paper, the problem of adaptive fault-tolerant tracking control for a class of uncertain nonlinear systems in the presence of input quantisation and unknown control direction is considered. By choosing a class of particular Nussbaum functions, an adaptive fault-tolerant control scheme is designed to compensate actuator faults and input quantisation while the control direction is unknown. Compared with the existing results, the proposed controller can directly compensate for the nonlinear term caused by actuator faults and the nonlinear decomposition on the quantiser without estimating its bound. Furthermore, via Barhalant's Lemma, it is proven that all the signals of the closed-loop system are globally uniformly bounded and the tracking error converges into a prescribed accuracy in prior. Finally, an illustrative example is used for verifying effectiveness of the proposed approach.     

Adaptive fuzzy ILC of nonlinear discrete-time systems with unknown dead zones and control directions

This paper presents an adaptive fuzzy iterative learning control (ILC) design for non-parametrized nonlinear discrete-time systems with unknown input dead zones and control directions. In the proposed adaptive fuzzy ILC algorithm, a fuzzy logic system (FLS) is used to approximate the desired control signal, and an additional adaptive mechanism is designed to compensate for the unknown input dead zone. In dealing with the unknown control direction of the nonlinear discrete-time system, a discrete Nussbaum gain technique is exploited along the iteration axis and applied to the adaptive fuzzy ILC algorithm. As a result, it is proved that the proposed adaptive fuzzy ILC scheme can drive the ILC tracking errors beyond the initial time instants into a tunable residual set as iteration number goes to infinity, and keep all the system signals bounded in the adaptive ILC process. Finally, a simulation example is used to demonstrate the feasibility and effectiveness of the adaptive fuzzy ILC scheme.     

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.     

不确定非线性多智能体系统的分布式容错协同控制

针对一类存在未知非线性的多智能体系统,研究具有执行器故障的“领导-跟随”协同控制问题。利用模糊逻辑系统逼近系统的未知非线性,通过设计故障估计器辨识系统的故障。在“跟随者”之间的通信网络为单向连通的情况下,提出分布式模糊容错协同控制器的设计方案,实现“跟随者”的状态跟踪“领导者”的状态。基于Lyapunov稳定性理论,证明系统的跟踪误差一致最终有界。仿真结果验证了所提出设计方法的有效性。     

虚拟控制系数未知的非完整系统的自适应神经网络控制

针对一类虚拟控制系数未知的多输入链式非完整控制系统,提出了一种自适应神经网络控制策略.在控制策略的设计中,采用了State-scaling与Backstepping技术相结合的方法.Nussbaum-type增益技术用来解决系统的控制方向完全未知的问题.所提出的自适应神经网络控制策略解决了由复杂系统所引起的奇异问题,并通过选择适当的控制参数,使闭环系统半全局一致有界,且系统的状态渐近收敛到包含原点的任意小的一个收敛域.一种基于切换策略的自适应控制方法解决了当x0(t0)=0时所引起的系统不可控问题.仿真结果验证了算法的有效性.     

Adaptive fuzzy control for unknown nonlinear time-delay systems with virtual control functions

In this paper, adaptive fuzzy control is presented for a class of unknown nonlinear timedelay systems with virtual control functions. By employing fuzzy logic systems and the technique of delay replacement, dynamic surface control (DSC) design approach can be carried out with both unknown delay signals and nonlinearities. This is different from the existing results, which are used to make limitations on the time-delays. It is proved that the proposed design method is able to guarantee semiglobal uniform ultimate boundedness (SGUUB) of all signals in the closed-loop system, with arbitrary small tracking error by appropriately choosing design constants.     

Adaptive inverse control for parametric strict feedback systems with unknown failures of hysteretic actuators

An adaptive compensation control scheme is proposed by using backstepping techniques for a class of uncertain nonlinear systems preceded by m hysteretic actuators, which exhibit unknown backlash nonlinearity and possibly experience unknown failures. An estimated smooth inverse of the actuator backlash is utilized in the controller design to compensate for the effects of the backlash and actuator failures. It is shown that the designed controllers can ensure all signals of closed‐loop system bounded for any failure pattern of hysteretic actuators and tracking performance is also maintained. Simulation studies confirm the effectiveness of the proposed controller, especially the improvement of system performances. Copyright © 2013 John Wiley & Sons, Ltd.     

分散自适应模糊滑模控制器的设计与分析

研究了一类具有函数控制增益的耦合大系统的分散自适应模糊控制问题 ,提出了能够利用专家的语言信息和数字信息的分散自适应模糊滑模控制器的设计方案 .通过理论分析 ,证明了分散自适应模糊控制系统是全局稳定的 ,跟踪误差可收敛到零的一个邻域内     

Adaptive decentralized fault‐tolerant tracking control for large‐scale nonlinear systems with input quantization

In this paper, an adaptive decentralized tracking control scheme is designed for large‐scale nonlinear systems with input quantization, actuator faults, and external disturbance. The nonlinearities, time‐varying actuator faults, and disturbance are assumed to exist unknown upper and lower bounds. Then, an adaptive decentralized fault‐tolerant tracking control method is designed without using backstepping technique and neural networks. In the proposed control scheme, adaptive mechanisms are used to compensate the effects of unknown nonlinearities, input quantization, actuator faults, and disturbance. The designed adaptive control strategy can guarantee that all the signals of each subsystem are bounded and the tracking errors of all subsystems converge asymptotically to zero. Finally, simulation results are provided to illustrate the effectiveness of the designed approach.     

一种统一的鲁棒自适应控制方法及近期自适应控制结果综述

针对离散/连续时间情况下时不变/时变多种不同的鲁棒自适应控制系统,基于归纳法提出一种统一的传统分析方法,该方法为鲁棒自适应控制器的设计提供了一般性的指导原则.在设计和实现鲁棒自适应控制器时要求具有与模型误差先验知识相关的假设,通过所提出的算法可以将该假设消除,使得已有的鲁棒自适应控制理论得到进一步发展.此外,通过稳定性分析证明了该算法对于更宽松边界的模型误差具有鲁棒性.最后,归纳总结了近期自适应控制方法在处理非光滑不确定性、执行器故障补偿、欠驱动非完整约束、分布式一致性和随机系统控制等问题上取得的代表性成果.