Robust adaptive fuzzy tracking control for a class of strict-feedback nonlinear systems based on backstepping technique

In this paper, the robust adaptive fuzzy tracking control problem is discussed for a class of perturbed strict-feedback nonlinear systems. The fuzzy logic systems in Mamdani type are used to approximate unknown nonlinear functions. A design scheme of the robust adaptive fuzzy controller is proposed by use of the backstepping technique. The proposed controller guarantees semi-global uniform ultimate boundedness of all the signals in the derived closed-loop system and achieves the good tracking performance. The possible controller singularity problem which may occur in some existing adaptive control schemes with feedback linearization techniques can be avoided. In addition, the number of the on-line adaptive parameters is not more than the order of the designed system. Finally, two simulation examples are used to demonstrate the effectiveness of the proposed control scheme.     

Fuzzy adaptive backstepping robust control for SISO nonlinear system with dynamic uncertainties

In this paper, a fuzzy adaptive backstepping design procedure is proposed for a class of nonlinear systems with three types of uncertainties: (i) nonlinear uncertainties; (ii) unmodeled dynamics and (iii) dynamic disturbances. The fuzzy logic systems are used to approximate the nonlinear uncertainties, nonlinear damping terms are used to counteract the dynamic disturbances and fuzzy approximation errors, and a dynamic signal is introduced to dominate the unmodeled dynamics. The derived fuzzy adaptive control approach guarantees the global boundedness property for all the signals and states, and at the same time, steers the output to a small neighborhood of the origin. Simulation studies are included to illustrate the effectiveness of the proposed approach.     

Direct adaptive fuzzy control of nonlinear strict-feedback systems

This paper focuses on adaptive fuzzy tracking control for a class of uncertain single-input /single-output nonlinear strict-feedback systems. Fuzzy logic systems are directly used to approximate unknown and desired control signals and a novel direct adaptive fuzzy tracking controller is constructed via backstepping. The proposed adaptive fuzzy controller guarantees that the output of the closed-loop system converges to a small neighborhood of the reference signal and all the signals in the closed-loop system remain bounded. A main advantage of the proposed controller is that it contains only one adaptive parameter that needs to be updated online. Finally, an example is used to show the effectiveness of the proposed approach.     

一类具有未建模动态的非线性系统模糊自适应鲁棒控制

针对一类单输入单输出未建模动态不确定非线性系统,提出一种模糊自适应backstepping控制方法.设计中利用模糊逻辑系统逼近系统的未知函数,应用非线性阻尼项抵消系统的非线性不确定项,通过引入一个动态信号克服未建模动态.该模糊自适应控制方法保证了整个闭环系统的有界性,输出信号可调节到零的小邻域内.仿真结果进一步验证了该方法的有效性.     

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.     

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.     

Robust adaptive fuzzy backstepping output feedback tracking control for nonlinear system with dynamic uncertainties

In this paper, an adaptive fuzzy output feedback control approach based on backstepping design is proposed for a class of SISO strict feedback nonlinear systems with unmeasured states, nonlinear uncertainties, unmodeled dynamics, and dynamical disturbances. Fuzzy logic systems are employed to approximate the nonlinear uncertainties, and an adaptive fuzzy state observer is designed for the states estimation. By combining backstepping technique with the fuzzy adaptive control approach, a stable adaptive fuzzy...     

Event-triggered adaptive fuzzy tracking control of nonlinear MIMO systems

This paper addresses the problem of an adaptive fuzzy event-triggered control (ETC) for uncertain multi-input and multi-output nonlinear systems. To reduce the communication burden of the network control systems, a novel state-dependent event-triggering condition is designed to decide when to update the controllers. By combining the backstepping and event-trigged techniques, the adaptive fuzzy ETC strategies are developed and the resulting closed-loop system is semi-global bounded. Finally, the analytical results are substantiated using simulation studies.     

一类不确定非线性系统的鲁棒自适应控制

针对一类MIMO不确定非线性系统的输出跟踪问题, 基于自适应反步法和滑模控制为其设计了鲁棒自适应控制器. 模型包含3种不确定性: 1) 参数不确定性; 2) 输入增益的不确定性; 3) 代表系统未建模动态和干扰的不确定函数, 该函数有界. 以非完整移动机械臂的输出跟踪控制为目标, 对其进行仿真实验, 实验结果表明所提出的控制算法是正确有效的.     

一类不确定非线性纯反馈系统的自适应鲁棒模糊控制

针对一类带有不确定性的非线性MIMO纯反馈系统,提出一种自适应鲁棒模糊控制方法,该方法放宽了已有文献对系统模型的限制条件,基于李雅普诺夫分析方法获得了控制输入和自适应律．在控制输入设计中,鲁棒控制项用于补偿逼近误差向量．通过选择适当的设计参数。提出的控制方法使得闭环系统的所有信号是一致有界的和跟踪误差向量的范数收敛到小的零邻域内．仿真结果表明了所提出方法的有效性．     

Robust controller design of a class of nonlinear time delay systems via backstepping method

The robust control problem is investigated for nonlinear time delay systems with triangular structure. The uncertain delay disturbances are bounded by nonlinear functions with unknown coefficients. Via the backstepping method, we construct a state feedback controller with the help of Razumikhin lemma. Based on Lyapunov stability theory, we show that the resulting closed-loop system is UUB stable.     

多变量非线性系统的间接模糊输出反馈自适应控制

针对一类多输入多输出非线性不确定系统，提出一种基于观测器的模糊间接自适应控制方法，并基于李亚普诺夫函数方法，导出了输出反馈控制律以及参数的自适应律，证明了整个控制方案不但能保证闭环系统稳定，而且取得了良好的跟踪控制性能。     

Robust backstepping for the Euler approximate model of sampled-data strict-feedback systems

Stabilization of uncertain sampled-data strict-feedback systems is addressed. The stability study is carried out on the Euler approximation of the exact discretized model of the plant. Firstly, a class of state-feedback controllers is developed that guarantees an input-to-state stability property for the closed-loop system. Additionally, assuming some hypotheses on the uncertain terms hold, a practical asymptotic stability property is ensured by designing an appropriate class of controllers.     

Neural adaptive control for a class of nonlinear systems with unknown deadzone

This paper focuses on the adaptive control of a class of nonlinear systems with unknown deadzone using neural networks. By constructing a deadzone pre-compensator, a neural adaptive control scheme is developed using backstepping design techniques. Transient performance is guaranteed and semi-globally uniformly ultimately bounded stability is obtained. Another feature of this scheme is that the neural networks reconstruction error bound is assumed to be unknown and can be estimated online. Simulation results are given to demonstrate the effectiveness of the proposed controller.     

Robust adaptive backstepping control for a class of uncertain nonlinear systems based on disturbance observers

In this paper, a novel robust adaptive control scheme for a class of uncertain nonlinear systems is proposed using disturbance observer and backstepping method.Firstly, a disturbance observer is developed using radial basis function(RBF) neural network.The parameter updated law of the RBF neural network is given for monitoring subsystem disturbance well.The robust adaptive control scheme is then presented with backstepping method based on the designed disturbance observer.Semiglobal uniform ultimate bounded...     

基于观测器的非线性互连系统的自适应模糊控制

针对一类不确定非线性MIMO互连系统,提出一种自适应模糊控制算法.通过设计观测器来估计系统的状态,因此不要求假设系统的状态是可测的.给出的自适应律只对不确定界进行在线调节,从而大大减轻了在线计算负担.该算法能够保证闭环系统的所有信号是一致有界的,并且跟踪误差指数收敛到一个小的零邻域内.仿真结果表明了算法的可行性.     

Adaptive stabilization of a class of uncertain switched nonlinear systems with backstepping control

In this paper, we focus on the problem of adaptive stabilization for a class of uncertain switched nonlinear systems, whose non-switching part consists of feedback linearizable dynamics. The main result is that we propose adaptive controllers such that the considered switched systems with unknown parameters can be stabilized under arbitrary switching signals. First, we design the adaptive state feedback controller based on tuning the estimations of the bounds on switching parameters in the transformed system, instead of estimating the switching parameters directly. Next, by incorporating some augmented design parameters, the adaptive output feedback controller is designed. The proposed approach allows us to construct a common Lyapunov function and thus the closed-loop system can be stabilized without the restriction on dwell-time, which is needed in most of the existing results considering output feedback control. A numerical example and computer simulations are provided to validate the proposed controllers.     

Robust tracking control of uncertain nonlinear systems with unknown control directions

A global robust tracking control design procedure is proposed for a class of uncertain nonlinear systems. The key point is that the signs of multiplicative uncertainties, the so-called control directions, are not assumed to be known a priori. The class of systems can be of arbitrary dynamic order and the unmatched additive uncertainties need not satisfy the global Lipschitz condition. It is proved that under the proposed control, all closed-loop states are bounded and the tracking error converges to any prescribed small neighborhood of the origin. The results of this paper enlarge the class of uncertain nonlinear systems for which global robust tracking control can be designed.     

Adaptive fuzzy tracking control of nonlinear time-delay systems with unknown virtual control coefficients

In this paper, a novel adaptive fuzzy control scheme is proposed for a class of uncertain single-input and single-output (SISO) nonlinear time-delay systems with the lower triangular form. Fuzzy logic systems are used to approximate unknown nonlinear functions, then the adaptive fuzzy tracking controller is constructed by combining Lyapunov-Krasovskii functionals and the backstepping approach. The proposed controller guarantees uniform ultimate boundedness of all the signals in the closed-loop system, while the tracking error converges to a small neighborhood of the origin. An advantage of the proposed control scheme lies in that the number of adaptive parameters is not more than the order of the systems under consideration. Finally, simulation studies are given to demonstrate the effectiveness of the proposed design scheme.