具有全状态约束和未建模动态的严格反馈系统有限时间自适应动态面控制

针对一类具有全状态约束、未建模动态和动态扰动的严格反馈非线性系统,通过构造非线性滤波器,并利用Young’s不等式,提出一种新的有限时间自适应动态面控制方法.引入非线性映射处理全状态约束,将有约束系统变成无约束系统,利用径向基函数逼近未知光滑函数,利用辅助系统产生的动态信号处理未建模动态.对于变换后的系统,利用改进的动态面控制和有限时间方法设计的控制器结构简单,移去现有有限时间控制中出现的“奇异性”问题,可加快系统的收敛速度.理论分析表明,闭环系统中的所有信号在有限时间内有界,全状态不违背约束条件.数值算例的仿真结果表明,所提出的自适应动态面控制方案是有效的.     

Adaptive optimal dynamic surface control of strict‐feedback nonlinear systems with output constraints

In this paper, an adaptive optimal control strategy is proposed for a class of strict‐feedback nonlinear systems with output constraints by using dynamic surface control. The controller design procedure is divided into two parts. One is the design of feedforward controller and the other is the design of optimal controller. To guarantee the satisfaction of output constraints in feedforward controller, nonlinear mapping is utilized to transform the constrained system into an unconstrained system. Neural‐network based adaptive dynamic programming algorithm is employed to approximate the optimal cost function and the optimal control law. By theoretical analysis, all the signals in the closed‐loop system are proved to be semi‐globally uniformly ultimately bounded and the output constraints are not violated. A numerical example illustrates the effectiveness of the proposed scheme.     

Robust adaptive output‐feedback control for nonlinear systems with output unmodeled dynamics

In this paper, for a class of uncertain nonlinear systems in the presence of inverse dynamics, output unmodeled dynamics and nonlinear uncertainties, a robust adaptive output‐feedback controller design is proposed by combining small‐gain theorem, changing supply function techniques with backstepping methods. It is shown that all the signals of the closed‐loop system are uniformly bounded in biased case, and the output can be regulated to a small neighborhood of the origin in unbiased case. Furthermore, under some additional assumptions, an asymptotical result is obtained. Copyright © 2007 John Wiley & Sons, Ltd.     

具有未建模动态系统的自适应动态面输出反馈控制

针对一类具有未建模动态和动态扰动且状态不可量测的非线性系统,利用神经网络逼近未知函数设计K-滤波器重构系统状态,提出一种自适应输出反馈控制策略。通过对未建模动态的新刻画,避免动态信号的引入。采用动态面设计方法,取消理论分析中产生的未知连续函数的估计,降低设计的复杂性。利用Lyapunov方法证明了闭环系统的所有信号是半全局一致终结有界的,并通过仿真结果验证了所提出方案的有效性。     

A neural composite dynamic surface control for pure‐feedback systems with unknown control gain signs and full state constraints

This paper investigates a composite neural dynamic surface control (DSC) method for a class of pure‐feedback nonlinear systems in the case of unknown control gain signs and full‐state constraints. Neural networks are utilized to approximate the compound unknown functions, and the approximation errors of neural networks are applied in the design of updated adaptation laws. Comparing the proposed composite approximation method with the conventional ones, a faster and better approximation performance result can be obtained. Combining the composite neural networks approximation with the DSC technique, an improved composite neural adaptive control approach is designed for the considered nonlinear system. Then, together with the Lyapunov stability theory, all the variables of the closed‐loop system are semiglobal uniformly ultimately bounded. The infringements of full state constraints can be avoided in the case of unknown control gain signs as well as unknown disturbances. Finally, two simulation examples show the effectiveness and feasibility of the proposed results.     

具有预设性能的切换系统输出反馈自适应动态面控制

本文针对一类具有未建模动态和预设性能的输出反馈非线性切换系统,提出基于公共Lyapunov函数法的自适应输出反馈动态面控制方案.通过设计K滤波器和观测器估计不可测量的状态.引入动态信号处理动态不确定性.利用Nussbaum函数解决增益符号未知的问题.神经网络用于逼近由设计过程和理论分析所产生的未知连续函数.引入性能函数和误差转换器将预设性能控制问题转换为稳定性问题.通过适当选取切换子系统的初值,并利用动态面控制系统证明的特点,证明了闭环切换系统所有信号半全局一致终结有界.仿真例子验证了所提方案的有效性.     

不确定非线性系统的鲁棒自适应输出反馈控制

基于自适应非线性阻尼,提出一种鲁棒自适应输出反馈控制方法。该方法适用于带有未建模动态、未知非线性、有界扰动、未知非线性参数和不确定控制系数的多输入多输出非线性系统。理论证明,在一定的假设条件下,该方法能保证闭环系统所有动态信号有界;不论有多少不确定非线性参数、多高阶的非线性系统,只需要一个自适应控制参数和观察参数;而且通过选择适当的控制器和观测器参数,能使控制误差和估计误差达到任意小。仿真结果表明了所提出方法的有效性。     

Adaptive prescribed performance tracking control for strict‐feedback nonlinear systems with zero dynamics

This paper focuses on the adaptive tracking control problem for strict‐feedback nonlinear systems with zero dynamics via prescribed performance. Based on polynomial fitting, an adjustable performance function is firstly proposed, whose parameters can be adjusted in real time according to the tracking error. Furthermore, an adaptive prescribed performance tracking controller is constructed via the backstepping method, which guarantees that all the states in the closed‐loop system are bounded. Meanwhile, the output tracking error falls within an adjustable performance boundary and asymptotically converges to zero. Simulation comparison demonstrates the advantages of the developed controller as follows: (1) the parameters of the adjustable performance function are adjusted online according to the tracking errors for a faster convergent performance boundary; (2) the steady‐state performance of the system is further optimized simultaneously.     

Distributed low-complexity output feedback tracking control for nonlinear multi-agent systems with unmodeled dynamics and prescribed performance

This paper investigates the prescribed performance distributed output consensus problem under directed graphs. With the utilisation of a filter, the original system of each follower can be converted into a strict-feedback system. Then, we design a prescribed performance output feedback distributed control protocol by applying the backstepping approach in the converted system. The proposed protocol can guarantee that the consensus tracking error of each agent evolves in predefined decaying bounds to achieve the prescribed performance, that is, the consensus tracking error of each agent converges to a predetermined residual set at a convergence rate no less than a prespecified value and exhibiting a maximum overshoot less than a preassigned constant. Moreover, during the process of consensus, all the signals in the closed-loop system are globally uniformly bounded. A simulation example is given to verify the effectiveness of the proposed control protocol.     

Prescribed performance adaptive neural output control for a class of switched nonstrict‐feedback nonlinear time‐delay systems: State‐dependent switching law approach

This paper investigates the tracking problem for a class of uncertain switched nonlinear delayed systems with nonstrict‐feedback form. To address this problem, by introducing a new common Lyapunov function (CLF), an adaptive neural network dynamic surface control is proposed. The state‐dependent switching rule is designed to orchestrate which subsystem is active at each time instance. In order to compensate unknown delay terms, an appropriate Lyapunov‐Krasovskii functional is considered in the constructing of the CLF. In addition, a novel switched neural network–based observer is constructed to estimate system states through the output signal. To maintain the tracking error performance within a predefined bound, a prescribed performance bound approach is employed. It is proved that by the proposed output‐feedback control, all the signals of the closed‐loop system are bounded under the switching law. Moreover, the transient and steady‐state tracking performance is guaranteed by the prescribed performance bound. Finally, the effectiveness of the proposed method is illustrated by two numerical and practical examples.     

Robust adaptive prescribed performance control for a class of nonlinear pure‐feedback systems

An adaptive prescribed performance control design procedure for a class of nonlinear pure‐feedback systems with both unknown vector parameters and unmodeled dynamics is presented. The unmodeled dynamics lie within some bounded functions, which are assumed to be partially known. A state transformation and an auxiliary system are proposed to avoid using the cumbersome formula to handle the nonaffine structure. Simultaneously, a parameter‐type Lyapunov function and L function are designed to ensure the prescribed performance of the pure‐feedback system. As illustrated by examples, the proposed adaptive prescribed performance control scheme is shown to guarantee global uniform ultimate boundedness. At the same time, this method not only guarantees the prescribed performance of the system but also makes the tracking error asymptotically close to a certain value or stable.     

Robust adaptive quantized DSC of uncertain pure‐feedback nonlinear systems with time‐varying output and state constraints

In this paper, the problem of neural adaptive dynamic surface quantized control is studied the first time for a class of pure‐feedback nonlinear systems in the presence of state and output constraint and unmodeled dynamics. The considered system is under the control of a hysteretic quantized input signal. Two types of one‐to‐one nonlinear mapping are adopted to transform the pure‐feedback system with different output and state constraints into an equivalent unconstrained pure‐feedback system. By designing a novel control law based on modified dynamic surface control technique, many assumptions of the quantized system in early literary works are removed. The unmodeled dynamics is estimated by a dynamic signal and approximated based on neural networks. The stability analysis indicates that all the signals in the closed‐loop system are semiglobally uniformly ultimately bounded, and the output and all the states remain in the prescribed time‐varying or constant constraints. Two numerical examples with a coarse quantizer show that the proposed approach is effective for the considered system.     

具有输入及状态未建模动态系统的输出反馈自适应控制

针对一类具有输入及状态未建模动态的非线性系统, 设计K滤波器来估计系统不可量测状态, 基于动态面控制技术并利用径向基函数神经网络的逼近能力, 提出一种输出反馈自适应跟踪控制方案. 利用Nussbaum 函数性质, 有效地解决了高频增益符号未知问题. 在控制器设计中引入规范化信号来约束输入未建模动态, 从而有效地抑制其产生的扰动. 通过理论分析证明了闭环控制系统是半全局一致终结有界的.

     

Robust adaptive control for a class of uncertain strict‐feedback nonlinear systems

In this paper, robust adaptive control is presented for a class of perturbed strict‐feedback nonlinear systems with both completely unknown control coefficients and parametric uncertainties. The proposed design method does not require the a priori knowledge of the signs of the unknown control coefficients. For the first time, the key technical Lemma is proven when the Nussbaum function is chosen by N(ζ)=ζ²cos(ζ), based on which the proposed robust adaptive scheme can guarantee the global uniform ultimate boundedness of the closed‐loop system signals. Simulation results show the validity of the proposed scheme. Copyright © 2008 John Wiley & Sons, Ltd.     

Disturbance-observer-based sampled-data adaptive output feedback control for a class of uncertain nonlinear systems

In this paper, a sampled-data adaptive output feedback controller is proposed for a class of uncertain nonlinear systems with unmeasured states, unknown dynamics and unknown time-varying external disturbances. To approximate uncertain nonlinear functions, radial basis function neural networks (RBFNNs) are employed. The state observer and the disturbance observer (DO) are constructed to estimate the unmeasured state and the external disturbance, respectively. Then, the sampled-data adaptive output feedback controller and adaptive laws are designed by using the backstepping design technique. The allowable sampling period T is derived to guarantee that all states of the resulting closed-loop system are semi-globally uniformly ultimately bounded. Finally, two simulation examples are presented to illustrate the effectiveness of the proposed approach.     

Neural network‐based adaptive dynamic surface control of uncertain nonlinear pure‐feedback systems

In this paper, by incorporating the dynamic surface control technique into a neural network‐based adaptive control design framework, we have developed a backstepping‐based control design for a class of nonlinear systems in pure‐feedback form with arbitrary uncertainty. The circular design problem which may exist in pure‐feedback systems is overcome. In addition, our development is able to eliminate the problem of ‘explosion of complexity’ inherent in the existing backstepping‐based methods. A stability analysis is given, which shows that our control law can guarantee the semi‐global uniformly ultimate boundedness of the solution of the closed‐loop system, and makes the tracking error arbitrarily small. Moreover, the proposed control design scheme can also be directly applied to the strict‐feedback nonlinear systems with arbitrary uncertainty. Copyright © 2010 John Wiley & Sons, Ltd.     

Robust output feedback control for a class of nonlinear systems with input unmodeled dynamics

The robust global stabilization problem of a class of uncertain nonlinear systems with input unmodeled dynamics is considered using output feedback, where the uncertain nonlinear terms satisfy a far more relaxed condition than the existing triangulartype condition. Under the assumption that the input unmodeled dynamics is minimum-phase and of relative degree zero, a dynamic output compensator is explicitly constructed based on the nonseparation principle. An example illustrates the usefulness of the proposed method.     

带有输出约束的柔性关节机械臂预设性能自适应控制

针对带有输出约束和模型不确定的柔性关节机械臂系统,提出一种基于时变障碍李雅普诺夫函数的预设性能自适应控制方法.通过构造指数衰减的时变约束边界,提出时变正切型障碍李雅普诺夫函数,能够同时适用于约束与非约束情况,进而拓宽传统对数型障碍李雅普诺夫函数的适用范围.此外,通过预先设置时变边界函数的相关参数,使得系统输出在初始阶段...     

Fault‐tolerant containment control of uncertain nonlinear systems in strict‐feedback form

This paper investigates the containment control problem of uncertain nonlinear strict‐feedback systems in the presence of actuator faults. The communication topology among the agents is directed, and there exists at least one leader that has a directed path to each follower. Based on fuzzy logic systems and the dynamic surface control technique, a fault‐tolerant containment control scheme is developed to guarantee that the outputs of all followers converge to the convex hull spanned by multiple dynamic leaders with bounded containment errors. The result is extended to a fault‐tolerant containment control with prescribed performance, such that the error surfaces are confined to predefined bounds regardless of actuator faults. Simulation results are provided to illustrate the effectiveness of the proposed methods. Copyright © 2016 John Wiley & Sons, Ltd.