输入受限四旋翼飞行器的模糊自适应动态面轨迹跟踪控制

针对输入受限条件下四旋翼飞行器的轨迹跟踪控制问题,考虑系统存在模型动态不确定和未知外界干扰的情况,提出一种模糊自适应动态面轨迹跟踪控制方法.该方法设计干扰观测器估计位置模型中复合扰动项,利用模糊系统逼近姿态模型中不确定项和外界干扰,并引入双曲正切函数和辅助系统处理输入受限问题,结合反演法和动态面技术设计轨迹跟踪控制器,以降低控制算法的复杂性,最后选取李雅普诺夫函数证明闭环系统所有信号一致最终有界.应用大疆M100飞行器模型进行仿真验证,结果表明所设计的控制器能够有效处理模型动态不确定和未知外界干扰问题,避免飞行器工作过程中因输入饱和导致执行器失效现象,精确地完成轨迹跟踪控制任务.     

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.     

Adaptive fuzzy fault-tolerant output feedback control of uncertain nonlinear systems with actuator faults

This article develops an adaptive fuzzy control method for accommodating actuator faults in a class of unknown nonlinear systems with unmeasured states. The considered faults are modelled as both loss of effectiveness and lock-in-place (stuck at unknown place). With the help of fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy adaptive observer is developed for estimating the unmeasured states. Combining the backstepping technique with the nonlinear tolerant-fault control theory, a novel adaptive fuzzy faults-tolerant control approach is constructed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are bounded and the tracking error between the system output and the reference signal converges to a small neighbourhood of zero by appropriate choice of the design parameters. Simulation results are provided to show the effectiveness of the control approach.     

含齿隙弹载舵机的全局反步模糊自适应控制

针对制导弹药电动舵机伺服系统中存在的齿隙、不确定参数及外部干扰,提出一种基于反步法的全局模糊自适应控制方法.首先,综合考虑上述非线性因素,分析描述齿隙的近似死区模型,建立含齿隙弹载舵机的双惯量机电模型,并将其引入采用"三闭环"结构的伺服系统中,构建非线性系统的状态空间;然后,采用模糊逻辑系统对齿隙等非线性因素进行自适应逼近与补偿控制,通过反步递推构造全系统Lyapunov函数,并运用Lyapunov第二法证明了整个闭环系统最终一致有界.仿真实验表明:较经典PID控制,该方法能更有效地削弱齿隙引起的传动力矩抖振与振荡冲击,既保证了系统的跟踪速度与控制精度,对不确定参数与外部干扰也具有较强的鲁棒性.     

Observer-based adaptive fuzzy fault-tolerant output feedback control of uncertain nonlinear systems with actuator faults

This paper develops an adaptive fuzzy control method for accommodating actuator faults in a class of unknown nonlinear systems with unmeasured states. The considered faults are modeled as lock-in-place (stuck at unknown place). With the help of fuzzy logic systems to approximate the unknown nonlinear functions, and K-filters are designed to estimate the unmeasured states. Combining the backstepping technique with the nonlinear fault-tolerant control theory, a novel adaptive fuzzy faults-tolerant control (FTC) approach is constructed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are bounded and the tracking error between the system output and the reference signal converges to a small neighborhood of zero by appropriate choice of the design parameters. Simulation results are provided to show the effectiveness of the control approach.     

Adaptive fuzzy backstepping control for a class of switched nonlinear systems with actuator faults

This paper investigates the problem of fault-tolerant control (FTC) for a class of switched nonlinear systems. These systems are under arbitrary switchings and are subject to both lock-in-place and loss-of-effectiveness actuator faults. In the control design, fuzzy logic systems are used to identify the unknown switched nonlinear systems. Under the framework of the backstepping control design, FTC, fuzzy adaptive control and common Lyapunov function stability theory, an adaptive fuzzy control approach is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed-loop switched system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error remains an adjustable neighbourhood of the origin. Two simulation examples are provided to illustrate the effectiveness of the proposed approach.     

Observer-based adaptive output-constrained control design of switched stochastic nonlinear systems with input saturation

In this article, the problem of adaptive fuzzy control for output-constrained switched stochastic nonlinear systems subject to input saturation is addressed. By employing the trigonometric function mapping method, the constrained systems are transformed into unconstrained ones, and the control goals of the original constrained systems are not affected. Meanwhile, an auxiliary system is established to deal with the issue of input saturation, and an observer is constructed to estimate the unmeasured states. Then, the unknown nonlinear functions in the system are approximated by the fuzzy logic systems (FLSs). Based on the backstepping technique and Lyapunov function method, an output feedback control strategy is designed, where the dynamic surface control technique is applied in the backstepping design process to overcome the issue of a large number of online calculations. The designed controller can guarantee that all the signals of the system satisfy bounded conditions, and the output can track given reference signals within a small error range. Finally, a simulation example is given to verify the effectiveness of the proposed control scheme.     

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.     

Actuator fault‐tolerant control of ocean surface vessels with input saturation

In this paper, an actuator robust fault‐tolerant control is proposed for ocean surface vessels with parametric uncertainties and unknown disturbances. Using the backstepping technique and Lyapunov synthesis method, the adaptive tracking control is first developed by incorporating the actuator configuration matrix and considering actuator saturation constraints. The changeable actuator configuration matrix caused by rotatable propulsion devices is considered. Next, the actuator fault‐tolerant control is developed for the case when faults occur in propulsion devices of the ocean surface vessel. Rigorous stability analysis is carried out to show that the proposed fault‐tolerant control can guarantee the stability of the closed‐loop system under certain actuator failure. Finally, simulation studies are given to illustrate the effectiveness of the proposed adaptive tracking control and fault‐tolerant control. Copyright © 2015 John Wiley & Sons, Ltd.     

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 fuzzy backstepping output feedback control of nonlinear time-delay systems with unknown high-frequency gain sign

In this paper, an adaptive fuzzy robust feedback control approach is proposed for a class of single-input and single-output (SISO) strict-feedback nonlinear systems with unknown nonlinear functions, time delays, unknown high-frequency gain sign, and without the measurements of the states. In the backstepping recursive design, fuzzy logic systems are employed to approximate the unknown smooth nonlinear functions, K-filters is designed to estimate the unmeasured states, and Nussbaum gain functions are introduced to solve the problem of unknown sign of high-frequency gain. By combining adaptive fuzzy control theory and adaptive backstepping design, a stable adaptive fuzzy output feedback control scheme is developed. It has been proven that the proposed adaptive fuzzy robust control approach can guarantee that all the signals of the closed-loop system are uniformly ultimately bounded and the tracking error can converge to a small neighborhood of the origin by appropriately choosing design parameters. Simulation results have shown the effectiveness of the proposed method.     

Event-triggered adaptive tracking control for nonlinear systems with input saturation and unknown control directions

This article is concerned with event-triggered adaptive tracking control design of strict-feedback nonlinear systems, which are subject to input saturation and unknown control directions. In the design procedure, a smooth nonlinear function is employed to approximate the saturation function so that the controller can be designed under the framework of backstepping. The Nussbaum gain technique is employed to address the issue of the unknown control directions. A predetermined time convergent performance function and a nonlinear mapping technique are introduced to guarantee that the tracking error can converge in the predetermined time with a fast convergence rate and a high accuracy. Then the event-triggered adaptive prescribed performance tracking control strategy is proposed, which not only ensures the boundedness of all the closed-loop signals and the convergence of tracking error but also reduces the communication burden from the controller to the actuator. At last, the simulation study further tests the availability of the proposed control strategy.     

Observer-Based Adaptive Fuzzy Tracking Control Using Integral Barrier Lyapunov Functionals for A Nonlinear System With Full State Constraints

A new fuzzy adaptive control method is proposed for a class of strict feedback nonlinear systems with immeasurable states and full constraints.The fuzzy logic system is used to design the approximator,which deals with uncertain and continuous functions in the process of backstepping design.The use of an integral barrier Lyapunov function not only ensures that all states are within the bounds of the constraint,but also mixes the states and errors to directly constrain the state,reducing the conservativeness of the constraint satisfaction condition.Considering that the states in most nonlinear systems are immeasurable,a fuzzy adaptive states observer is constructed to estimate the unknown states.Combined with adaptive backstepping technique,an adaptive fuzzy output feedback control method is proposed.The proposed control method ensures that all signals in the closed-loop system are bounded,and that the tracking error converges to a bounded tight set without violating the full state constraint.The simulation results prove the effectiveness of the proposed control scheme.     

Adaptive compensation control for special actuator circumstances with input quantization

In this article, considering actuator constraints and possible failures, an adaptive compensation control scheme is developed to realize tracking control for a class of uncertain nonlinear systems with quantized inputs. A new variable is generated to evaluate the effect of actuator saturation and is used in the process of controller design to compensate for the influence of actuator saturation constraint. Moreover, the controller is able to show certain accommodation capability to tolerate possible actuator failures and input quantization error via integrating parameter update process of unknown fault constants into adaption of parametric uncertainties under the backstepping procedure. Specifically, actuator saturation effect and possible actuator failures as well as input quantization error can be dealt with uniformly under the framework of the proposed scheme and the control system has certain robustness to external disturbances. It is proved that all the signals of the closed‐loop system are ensured to be bounded and the tracking error is enabled to converge toward a compact set, which is adjustable by tuning design parameters. Finally, experiments are carried out on an active suspension plant to illustrate the effectiveness of the proposed control scheme.     

倒立摆的自适应积分反步控制策略

针对直线单级倒立摆在模型参数不确定和外部扰动情况下的稳定控制问题,提出一种自适应积分反步控制策略。采用拉格朗日方程建立倒立摆系统的运动学模型,为减少稳态误差,将误差积分项引入反步法,设计了倒立摆的控制器;对含有未知参数的系统非线性状态微分方程,设计适当的Lyapunov函数推导出系统未知参数的自适应更新律,削弱了参数不确定性的影响。将自适应积分反步控制与一般的反步法控制、模糊控制及神经网络控制的仿真结果进行了对比,并在LabVIEW开发环境下进行了实物实验。结果表明,自适应积分反步法可以较为迅速且精确地完成稳定控制,较好地克服系统参数不确定及外部扰动的影响,具有较强的鲁棒性。     

Adaptive fuzzy fault-tolerant attitude control of spacecraft

This paper investigates the attitude control of spacecraft in the presence of unknown mass moment of inertia matrix, external disturbances, actuator failures, and control input constraints. A robust adaptive controller is proposed with the utilization of fuzzy logic and backstepping techniques. The unit quaternion is employed to describe the attitude of spacecraft for global representation without singularities. The system uncertainty is estimated by introducing a fuzzy logic system. The adaptive mechanism has only two parameters to be adapted on-line because the adaptive law of the proposed controller is derived from the norm of the weight matrix. The stability of the closed-loop system is guaranteed by Lyapunov direct approach. Results of numerical simulations state that the proposed controller is successful in achieving high attitude performance in the presence of parametric uncertainties, external disturbances, actuator failures, and control input constraints.     

Adaptive fuzzy neural network finite-time command filtered control of n-link robotic systems with actuator saturation

The finite time tracking control of n-link robotic system is studied for model uncertainties and actuator saturation. Firstly, a smooth function and adaptive fuzzy neural network online learning algorithm are designed to address the actuator saturation and dynamic model uncertainties. Secondly, a new finite-time command filtered technique is proposed to filter the virtual control signal. The improved error compensation signal can reduce the impact of filtering errors, and the tracking errors of system quickly converge to a smaller compact set within finite time. Finally, adaptive fuzzy neural network finite-time command filtered control achieves finite-time stability through Lyapunov stability criterion. Simulation results verify the effectiveness of the proposed control.     

一类状态/输入受限的不确定非仿射非线性系统 鲁棒自适应backstepping控制

针对一类状态/输入受限的不确定严格反馈非仿射非线性系统跟踪控制问题,提出一种鲁棒自适应backstepping控制策略.在保证系统精度的前提下,对状态/输入受限的非仿射系统进行Taylor级数在线展开,得到其仿射形式;为保证系统复合扰动在线准确逼近,提出基于投影算子的递归扰动模糊神经网络干扰观测器(RPFNNDO);在考虑不确定系统存在状态受限和输入饱和等因素下,结合障碍Lyapunov函数、tanh函数及Nussbaum函数,利用backstepping方法设计控制器,并采用Lyapunov稳定理论分析闭环系统稳定性.应用于无人机航迹控制的仿真结果验证了所提方法的有效性.     

Adaptive Control of Partially Known Systems and Application To Active Suspensions

In this paper, an adaptive control method is proposed for systems whose structures can be divided into a known part and an unknown part. A non‐adaptive control design, such as H∞ control design can be introduced into the known part of the system, and adaptive control can cope with the unknown part to realize the property designed by non‐adaptive control. This is achieved by means of backstepping. This method is applied to the control design of an active suspension system for a railway vehicle, which is divided into two parts: a main car body part and an actuator part. Some simulation results of the control system designed using H∞ control for the body part and adaptive control for the actuator part are provided.     

An adaptive fuzzy design for fault-tolerant control of MIMO nonlinear uncertain systems

This paper presents a novel control method for accommodating actuator faults in a class of multiple-input multiple-output (MIMO) nonlinear uncertain systems.The designed control scheme can tolerate both the time-varying lock-in-place and loss of effectiveness actuator faults.In each subsystem of the considered MIMO system,the controller is obtained from a backstepping procedure;an adaptive fuzzy approximator with minimal learning parameterization is employed to approximate the package of unknown nonlinear functions in each design step.Additional control effort is taken to deal with the approximation error and external disturbance together.It is proven that the closed-loop stability and desired tracking performance can be guaranteed by the proposed control scheme.An example is used to show the effectiveness of the designed controller.