Distributed Containment Control of Networked Nonlinear Second-order Systems With Unknown Parameters

In this paper, we study the containment control problem for nonlinear second-order systems with unknown parameters and multiple stationary/dynamic leaders. The topologies that characterize the interaction among the leaders and the followers are directed graphs. Necessary and sufficient criteria which guarantee the control objectives are established for both stationary leaders (regulation case) and dynamic leaders (dynamic tracking case) based protocols. The final states of all the followers are exclusively determined by the initial values of the leaders and the topology structures. In the regulation case, all the followers converge into the convex hull spanned by the leaders, while in the dynamic tracking case, not only the positions of the followers converge into the convex hull but also the velocities of the followers converge into the velocity convex hull of the leaders. Finally, all the theoretical results are illustrated by numerical simulations.      

Distributed containment control for nonlinear multiagent systems in pure‐feedback form

In this paper, the problem of distributed containment control for pure‐feedback nonlinear multiagent systems under a directed graph topology is investigated. The dynamics of each agent are molded by high‐order nonaffine pure‐feedback form. Neural networks are employed to identify unknown nonlinear functions, and dynamic surface control technique is used to avoid the problem of explosion of complexity inherent in backstepping design procedure. The Frobenius norm of the ideal neural network weighting matrices is estimated, which is helpful to reduce the number of the adaptive tuning law and alleviate the networked communication burden. The proposed distributed containment controllers guarantee that all signals in the closed‐loop systems are cooperatively semiglobally uniformly ultimately bounded, and the outputs of followers are driven into a convex hull spanned by the multiple dynamic leaders. Finally, the effectiveness of the developed method is demonstrated by simulation examples.     

控制方向未知的高次非线性系统的鲁棒自适应控制

研究了一类具有不可控不稳定线性化的非线性系统的自适应控制问题.该类系统的控制方向未知且含有不确定时变非线性参数.应用Nussbaum-type增益技术和adding a power integrator递推设计方法,设计了一种鲁棒自适应状态反馈控制器.所设计的控制器能够保证闭环系统的所有信号全局一致有界,且系统的状态渐近趋于零.除了假设未知参数及不确定性有界外,所设计的控制策略不需要控制系数的任何先验知识.仿真例子验证了算法的有效性.     

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.     

非线性系统的神经网络鲁棒自适应跟踪控制

针对一类具有未知非线性函数和未知虚拟系数非线性函数的二阶非线性系统,提出了一种神经网络鲁棒自适应输出跟踪控制方法.用李雅普诺夫稳定性分析方法证明了本文的神经网络自适应控制器能够使受控系统内的所有信号均为有界.选择的神经网络权值调整规律可以防止自适应控制中的参数漂移.     

Adaptive tracking control of nonlinear systems with dynamic uncertainties using neural network

In this paper, an adaptive neural tracking control approach is proposed for a class of nonlinear systems with dynamic uncertainties. The radial basis function neural networks (RBFNNs) are used to estimate the unknown nonlinear uncertainties, and then a novel adaptive neural scheme is developed, via backstepping technique. In the controller design, instead of using RBFNN to approximate each unknown function, we lump all unknown functions into a suitable unknown function that is approximated by only a RBFNN in each step of the backstepping. It is shown that the designed controller can guarantee that all signals in the closed-loop system are semi-globally bounded and the tracking error finally converges to a small domain around the origin. Two examples are given to demonstrate the effectiveness of the proposed control scheme.     

A low‐complexity design for distributed containment control of networked pure‐feedback systems and its application to fault‐tolerant control

This paper addresses a low‐complexity distributed containment control problem and its extension to fault‐tolerant control for networked nonlinear pure‐feedback systems under a directed graph. The multiple dynamic leaders are neighbors of only a subset of the followers described by completely non‐affine multi‐input multi‐output pure‐feedback dynamics. It is assumed that all followers' nonlinearities are heterogeneous and unknown. The proposed containment controller is implemented by using only error surfaces integrated by performance bounding functions and does not require any differential equations for compensating uncertainties and faults. Thus, compared with the previous containment control approaches for multi‐agent systems with unknown non‐affine nonlinearities, the distributed containment control structure is simplified. In addition, it is shown that the proposed control scheme can be applied to the fault‐tolerant containment control problem in the presence of unexpected system and actuator faults, without reconstructing any control structure. It is shown from Lyapunov stability theorem that all followers nearly converge to the dynamic convex hull spanned by the dynamic leaders and the containment control errors are preserved within certain given predefined bounds. Copyright © 2016 John Wiley & Sons, Ltd.     

Observer-based fuzzy adaptive fault control for a class of MIMO nonlinear systems

In this paper, the fault-tolerant control (FTC) problem is investigated for a class of multi-input multiple output nonlinear systems with time-varying delays, and an active FTC method is proposed. The controlled system contains unknown nonlinear functions, unknown control gain functions and actuator faults, which integrates time-varying bias and gain faults. Then, fuzzy logic systems are used to approximate the unknown nonlinear functions and unknown control gain functions, fuzzy adaptive observers are used for fault detection and isolation. Further, based on the obtained information, an accommodation method is proposed for compensating the actuator faults. It is shown that all the variables of the closed-loop system are semi-globally uniformly bounded, the tracking error converges to an arbitrary small neighbourhood of the origin. A simulation is given to demonstrate the effectiveness of the proposed approach.     

Robust H∞ containment control for uncertain multi-agent systems with inherent nonlinear dynamics

This article considers the distributed containment control problem of nonlinear multi-agent systems subject to parameter uncertainties and external disturbances. An appropriate controlled output function is defined to quantitatively analyse the effect of external disturbances on the containment control problem. By employing robust H_∞ control approach, sufficient conditions in terms of linear matrix inequalities (LMIs) are derived to ensure that all followers asymptotically converge to the convex hull spanned by the leaders with the prescribed H_∞ performance under fixed topology. Moreover, the unknown feedback matrix of the proposed protocol is determined by solving only two LMIs with the same dimensions as a single agent. Finally, a numerical example is provided to demonstrate the effectiveness of our theoretical results.     

一类不确定非仿射非线性系统自适应模糊控制

针对一类非仿射非线性系统提出了自适应模糊控制方法,该方法把不确定非线性系统表示为定常线性子系统加非线性项的形式,然后采用模糊逻辑系统设计补偿器来消除非线性项的影响。引入时变死区函数对模糊逻辑系统中的未知参数进行自适应调节,并对时变死区设计了自适应律。证明了该方法可使闭环系统的所有信号均有界,且使跟踪误差收敛到原点的小邻域内。仿真结果表明了该方法的有效性。     

Adaptive neural control for a class of uncertain nonlinear systems with unknown time delay

A neural network (NN)‐based robust adaptive control design scheme is developed for a class of nonlinear systems represented by input–output models with an unknown nonlinear function and unknown time delay. By approximating on‐line the unknown nonlinear functions with a three‐layer feedforward NN, the proposed approach does not require the unknown parameters to satisfy the linear dependence condition. The control law is delay independent and possible controller singularity problem is avoided. It is proved that with the proposed neural control law, all the signals in the closed‐loop system are semiglobally bounded in the presence of unknown time delay and unknown nonlinearity. A simulation example is presented to demonstrate the method. Copyright © 2008 John Wiley & Sons, Ltd.     

Adaptive output-feedback control for a class of nonlinear systems with actuator failures and input quantisation

In this paper, an adaptive output feedback control technique is proposed for a class of nonlinear systems with unknown parameters, unknown nonlinear functions, quantised input and possible actuator failures up to infinity. A modified backstepping approach is proposed by the use of high-gain K-filters, hyperbolic tangent function property and bound-estimation approach to compensate for the effect of possible number of actuator failures up to infinity, input quantisation and unknown nonlinear functions. It is proved both mathematically and by simulation that with the proposed controller, all the signals of the closed-loop system are globally bounded despite of input quantisation, unknown nonlinear functions and possible number of actuator failures up to infinity.     

Command-filter-based distributed containment control of nonlinear multi-agent systems with actuator failures

In this paper, the problem of distributed containment fault-tolerant control for a class of nonlinear multi-agent systems in strict-feedback form is studied. The considered nonlinear multi-agent systems are subject to unknown nonlinear functions and actuator faults with loss of effectiveness and lock-in-place. By resorting to the universal approximation capability of fuzzy logical systems, the command filtered backstepping technique and nonlinear fault-tolerant control theory, distributed controllers are designed recursively. From the Lyapunov stability theory, it is proved that all signals of the resulting closed-loop systems are cooperatively semi-globally uniformly ultimately bounded and the containment errors converge to a small neighbourhood of origin by properly tuning the design parameters. Finally, a numerical example is provided to show the effectiveness of the proposed control method.     

一类高阶非线性不确定系统自适应稳定控制

研究了一类高阶非线性不确定性系统的自适应稳定控制设计问题.因该系统的非线性程度高,其控制系数不等同、符号已知、但数值未知,故在此之前其稳定控制设计问题没有得到解决.本文应用自适应技术,结合设计参数的适当选取,从而得到了设计该类非线性系统状态反馈稳定控制器的新方法,并基于反推技术,给出了稳定控制器的设计步骤.所设计的状态反馈控制器使得闭环系统的状态全局渐近收敛于零,其余闭环信号一致有界.最后通过一个仿真例子说明了控制设计方法的有效性.     

Set membership inversion and robust control from data of nonlinear systems

A set membership method for right inversion of nonlinear systems from data is proposed in the paper. Both the cases where the system to invert is known or unknown and therefore identified from data are addressed. The method does not require the invertibility of the regression function describing the system and ensures tight bounds on the inversion error. In the case of unknown system, the method allows the derivation of a robust right‐inverse, guaranteeing the inversion error bound for all the systems belonging to the uncertainty set which can be defined from the available prior and experimental information. Based on such a set membership inversion, two methods for robust control of nonlinear systems from data are introduced: nonlinear feed‐forward control (NFFC) and nonlinear internal model control (NIMC). Both the design methods ensure robust stability and bounded tracking errors for all the systems belonging to the involved uncertainty set. Two applicative examples of robust control from data are presented: NFFC control of semi‐active suspension systems and NIMC control of vehicle lateral dynamics.Copyright © 2013 John Wiley & Sons, Ltd.     

Robust control approach for input–output linearizable nonlinear systems using high‐gain disturbance observer

This paper addresses a robust control approach for a class of input–output linearizable nonlinear systems with uncertainties and modeling errors considered as unknown inputs. As known, the exact feedback linearization method can be applied to control input–output linearizable nonlinear systems, if all the states are available and modeling errors are negligible. The mentioned two prerequisites denote important problems in the field of classical nonlinear control. The solution approach developed in this contribution is using disturbance rejection by applying feedback of the uncertainties and modeling errors estimated by a specific high‐gain disturbance observer as unknown inputs. At the same time, the nonmeasured states can be calculated from the estimation of the transformed system states. The feasibility and conditions for the application of the approach on mechanical systems are discussed. A nonlinear multi‐input multi‐output mechanical system is taken as a simulation example to illustrate the application. The results show the robustness of the control design and plausible estimations of full‐rank disturbances.Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

Two‐stage stability control for strict‐feedback systems with input delays and input nonlinear uncertainties

In this paper, a two‐stage control procedure is proposed for stabilization of a class of strict‐feedback systems with unknown constant time delays and nonlinear uncertainties in the input. A nominal controller is first designed to compensate input time delays without considering input nonlinear uncertainties. Extended from backstepping algorithm, input delay compensation is realized by means of predicted states that are computed through integration of cascaded system dynamics, making the nominal closed‐loop system asymptotically stable. Based on the nominal controller presented for the input delay system, a multi‐timescale system is subsequently developed to estimate the unknown input nonlinearity and make the estimate approach the nominal control input as fast as possible. It is proved that the proposed control scheme can make states of the strict‐feedback systems converge to zero and all the signals of the closed‐loop systems are guaranteed to be bounded in the presence of input time delays and nonlinear uncertainties. Simulation verification is carried out to illuminate the effectiveness of the proposed control approach.     

Adaptive output feedback control of a class of uncertain nonlinear systems with unknown time delays

This article studies the adaptive output feedback control problem of a class of uncertain nonlinear systems with unknown time delays. The systems considered are dominated by a triangular system without zero dynamics satisfying linear growth in the unmeasurable states. The novelty of this article is that a universal-type adaptive output feedback controller is presented to time-delay systems, which can globally regulate all the states of the uncertain systems without knowing the growth rate. An illustrative example is provided to show the applicability of the developed control strategy.     

Fast terminal sliding‐mode finite‐time tracking control with differential evolution optimization algorithm using integral chain differentiator in uncertain nonlinear systems

This paper presents a fast terminal sliding‐mode tracking control for a class of uncertain nonlinear systems with unknown parameters and system states combined with time‐varying disturbances. Fast terminal sliding‐mode finite‐time tracking systems based on differential evolution algorithms incorporate an integral chain differentiator (ICD) to feedback systems for the estimation of the unknown system states. The differential evolution optimization algorithm using ICD is also applied to a tracking controller, which provides unknown parametric estimation in the limitation of unknown system states for trajectory tracking. The ICD in the tracking systems strengthens the tracking controller robustness for the disturbances by filtering noises. As a powerful finite‐time control effort, the fast terminal sliding‐mode tracking control guarantees that all tracking errors rapidly converge to the origin. The effectiveness of the proposed approach is verified via simulations, and the results exhibit high‐precision output tracking performance in uncertain nonlinear systems.