Distributed prescribed performance control for consensus output tracking of nonlinear semi-strict feedback systems using finite-time disturbance observers

The distributed consensus output tracking problem is dealt with for a class of nonlinear semi-strict feedback systems in the presence of mismatched nonlinear uncertainties, external disturbances and uncertain nonlinear virtual control coefficients of the subsystems. The systems are under a directed communication graph, where the leader node is the root. The controller is designed in a backstepping manner, and the dynamic surface technique is adopted to avoid direct differentiation. At each step of virtual controller design, a prescribed performance controller is constructed to achieve prescribed transient performance so that the system states remain in the feasible domain. Then each virtual controller is enhanced by a finite-time disturbance observer which estimates the disturbance term in a finite-time. The properties of the control system are analysed theoretically. It is clarified that the prescribed performance control technique ensures that the system signals stay in the feasible domain, whereas sufficiently small ultimate control errors can be achieved by the finite-time disturbance observers. Finally, the performance of the proposed methods is confirmed by numerical studies.     

Robust control of nonlinear semi‐strict feedback systems using finite‐time disturbance observers

The output tracking controller design problem is dealt with for a class of nonlinear semi‐strict feedback systems in the presence of mismatched nonlinear uncertainties, external disturbances, and uncertain nonlinear virtual control coefficients of the subsystems. The controller is designed in a backstepping manner, and to avoid the shortcoming of ‘explosion of terms’, the dynamic surface control technique that employs a group of first‐order low‐pass filters is adopted. At each step of the virtual controller design, a robust feedback controller employing some effective nonlinear damping terms is designed to guarantee input‐to‐state practical stable property of the corresponding subsystem, so that the system states remain in the feasible domain. The virtual controller is enhanced by a finite‐time disturbance observer that estimates the disturbance term in a finite‐time. The properties of the composite control system are analyzed theoretically. Furthermore, by exploiting the cascaded structure of the control system, a simplified robust controller is proposed where only the first subsystem employs a disturbance observer. The performance of the proposed methods is confirmed by numerical examples. Copyright © 2017 John Wiley & Sons, Ltd.     

Quasi-finite-time control for high-order nonlinear systems with mismatched disturbances via mapping filtered forwarding technique

In this study, a quasi-finite-time control method for designing stabilising control laws is developed for high-order strict-feedback nonlinear systems with mismatched disturbances. By using mapping filtered forwarding technique, a virtual control is designed to force the off-the-manifold coordinate to converge to zero in quasi-finite time at each step of the design; at the same time, the manifold is rendered insensitive to time-varying, bounded and unknown disturbances. In terms of standard forwarding methodology, the algorithm proposed here not only does not require the Lyapunov function for controller design, but also avoids to calculate the derivative of sign function. As far as the dynamic performance of closed-loop systems is concerned, we essentially obtain the finite-time performances, which is typically reflected in the following aspects: fast and accurate responses, high tracking precision, and robust disturbance rejection. Spring, mass, and damper system and flexible joints robot are tested to demonstrate the proposed controller performance.     

Robust backstepping output tracking control for SISO uncertain nonlinear systems with unknown virtual control coefficients

The output tracking controller design problem is dealt with for a class of nonlinear strict-feedback form systems in the presence of nonlinear uncertainties, external disturbance, unmodelled dynamics and unknown time-varying virtual control coefficients. A new method based on signal compensation is proposed to design a linear time-invariant robust controller, which consists of a nominal controller and a robust compensator. It is shown that the closed-loop control system with a controller designed by the proposed method has robust asymptotical practical tracking property for any bounded initial conditions and robust tracking transient property if all initial states are zero.     

Robust‐decentralized tracking control for a class of uncertain MIMO nonlinear systems with time‐varying delays

A new control design method based on signal compensation is proposed for a class of uncertain multi‐input multi‐output (MIMO) nonlinear systems in block‐triangular form with nonlinear uncertainties, unknown virtual control coefficients, strongly coupled interconnections, time‐varying delays, and external disturbances. By this method, the controller design is performed in a backstepping manner. At each step of backstepping procedure, a nominal virtual controller is first designed to get desired output tracking for the nominal disturbance‐free subsystem, and then a robust virtual compensator is designed to restrain the effect of the uncertainties, delays involved in the subsystem, and the couplings among the subsystems. The designed controller is linear and time‐invariant, so the explosion of complexity in the control law is avoid. It is proved that robust stability and robust practical tracking property of the closed‐loop system can be ensured, and the tracking errors can be made as small as desired. Copyright © 2013 John Wiley & Sons, Ltd.     

一类机械臂系统自适应有限时间有界H∞跟踪控制

考虑一种电机驱动的单连杆机械臂系统在受到输出约束时的自适应有限时间H∞跟踪控制问题.一个有限时间有界H∞性能的新概念被提出,并结合障碍Lyapunov函数(BLF)、神经网络自适应技术、有限时间控制理论和H∞控制理论,提出了一种该系统在输出受限条件下的自适应神经有限时间有界H∞跟踪控制器设计方法,避免了许多有限时间控制...     

基于干扰观测器的一类不确定仿射非线性系统有限时间收敛backstepping控制

针对一类不确定仿射非线性系统的跟踪控制问题,提出一种基于干扰观测器的有限时间收敛backstepping控制方法.为增强小脑模型(CMAC)泛化和学习能力,将非对称高斯函数和模糊理论相结合,给出非对称模糊CMAC结构,设计干扰观测器实现系统未知复合干扰在线准确逼近;基于非对称模糊CMAC干扰观测器,给出有限时间收敛backstepping控制器设计步骤,利用Lyapunov稳定理论证明闭环系统稳定性,其中采用非线性微分器获取虚拟控制量滤波和微分信息以避免backstepping设计中的微分“膨胀问题”,设计辅助系统修正因微分器带来的误差对系统跟踪性能影响,引入基于障碍型函数的自适应滑模鲁棒项抑制复合干扰估计偏差对跟踪误差的影响;将所提方法应用于无人机飞行控制仿真实验,结果表明所提方法的有效性.     

一种非线性多环递归自适应跟踪控制

针对控制输入有界的变参数广义高阶非线性系统跟踪控制问题,给出一种多环递归跟踪的鲁棒控制方法.通过分层引入虚拟跟踪器,将高阶系统分解为多个独立子系统;内环虚拟跟踪器使内环输出指数收敛于外环虚拟输入,最内环设计自适应控制器补偿参数摄动和外部干扰,并保证输出指数收敛于外环虚拟输入;多环递归跟踪实现系统输出精确跟踪期望输入,理论证明闭环系统的全局渐近收敛性.数值仿真验证了多环跟踪控制器的可行性和合理性.     

Robust Finite-time Attitude Tracking Control of Rigid Spacecraft Under Actuator Saturation

This paper investigates the robust finite-time attitude tracking control problem for rigid spacecraft considering the modeling uncertainty, external disturbance and actuator saturation. An auxiliary system is proposed to directly compensate for the saturated control input. First, the basic controller is formulated based on the fast nonsingular terminal sliding mode surface (FNTSMS), the fast-TSM-type reaching law and the auxiliary system in the presence of upper bounded external disturbance. Then, when facing system uncertainty which consists of both modeling uncertainty and external disturbance and has upper bounded first derivative, the extended state observer (ESO) is associated with the first controller to improve the robustness of control system. Furthermore, to handle more general system uncertainty which is upper bounded by a polynomial function of the closed-loop system states, a continuous adaptive controller is designed to compensate for the total system uncertainty on line. The proposed controllers are able to deal with system uncertainty, input singularity and actuator saturation, while simultaneously providing fast finite-time convergence speed for the control system. And the problems of complex parameters selection process and repeated differentiations of nonlinear functions can be avoided. Rigorous stability analyses are given via the Lyapunov stability theory and digital simulations are conducted to illustrate the effectiveness of the proposed controllers.     

串级连续搅拌反应釜的有限时间命令滤波控制

针对串级连续搅拌反应釜系统的快速精准跟踪控制问题,利用自适应反步控制方法、模糊逻辑系统、命令滤波器以及有限时间控制技术设计串级连续搅拌反应釜系统的有限时间命令滤波控制器.其中,自适应反步方法使系统控制器的设计更简单;模糊逻辑系统通过逼近系统模型中的复杂非线性函数使控制器的在线计算量更小;命令滤波器解决了经典反步法带来的“计算爆炸”的问题;有限时间控制方法能够使系统被控量更迅速地跟踪其参考值; Lyapunov稳定性分析证明了系统的稳定性.通过Matlab实例仿真验证所设计控制器的有效性和可行性,为有限时间命令滤波控制技术在实际串级连续搅拌反应釜过程中的应用提供指导.与现有控制方法相比,所提出的控制策略具有控制器结构简单、在线计算复杂度小、跟踪速度快以及无静差的优点.     

基于非线性干扰观测器的翼伞鲁棒反步跟踪控制

针对干扰条件下的无人翼伞飞行器路径跟踪控制问题,提出一种基于非线性干扰观测器的反馈增益鲁棒反步控制方法.采用二阶跟踪-微分器设计干扰观测器对系统复合干扰进行估计和补偿,设计了反馈增益反步跟踪控制律,通过合理设计增益参数,消除了部分复杂非线性项,避免了虚拟量高阶导数问题,简化了控制器形式.根据Lyapunov理论设计鲁棒反馈补偿项,在保证稳定性的同时提高了系统的鲁棒性.仿真实验结果验证了所提出方法的有效性.     

Dynamic surface control approach to adaptive robust control of nonlinear systems in semi-strict feedback form

This article considers the adaptive robust control of a class of single-input-single-output nonlinear systems in semi-strict feedback form using radial basis function (RBF) networks. It is well known that the standard backstepping design may suffer from “explosion of terms”. To overcome this problem, the recently developed dynamic surface control technique which employs a first-order low-pass filter at each step of the backstepping design procedure is generalized to the nonlinear system under study. Our attention is paid to achieve guaranteed transient performance of the adaptive controller. At each step of design, a feedback controller strengthened by nonlinear damping terms to counteract nonlinear uncertainties is designed to guarantee input-to-state practical stability of the corresponding subsystem, and then parameter adaptations are introduced to reduce the ultimate error bound. Furthermore, for the output trajectory tracking problem, it is recommended to adopt the partial adaptation policy to reduce the computational burden due to “curse of dimension” of the RBF networks. Finally, numerical examples are included to verify the results of theoretical analysis.     

具有非匹配扰动的非线性变参数系统模型参考跟踪控制

本文研究了一类含有非匹配扰动的非线性变参数系统的跟踪控制问题.首先,设计非线性扰动观测器用于估计系统所受到的未知扰动.其次,在前馈–反馈跟踪控制器中引入扰动补偿控制项,提出一种基于扰动观测器的跟踪控制策略.利用依赖于状态和时变参数的线性矩阵不等式,导出保证闭环系统输入–状态稳定的充分条件,进而运用平方和凸优化技术解析地构造出扰动观测器和跟踪控制器.通过理论证明,所设计的控制策略能够实现非线性变参数系统输出对参考模型输出的跟踪,消除输出通道中非匹配扰动的影响.最后,由数值仿真例子验证了所提方法的有效性.     

Distributed adaptive output feedback tracking control for a class of uncertain nonlinear multi-agent systems

This paper addresses the distributed output feedback tracking control problem for multi-agent systems with higher order nonlinear non-strict-feedback dynamics and directed communication graphs. The existing works usually design a distributed consensus controller using all the states of each agent, which are often immeasurable, especially in nonlinear systems. In this paper, based only on the relative output between itself and its neighbours, a distributed adaptive consensus control law is proposed for each agent using the backstepping technique and approximation technique of Fourier series (FS) to solve the output feedback tracking control problem of multi-agent systems. The FS structure is taken not only for tracking the unknown nonlinear dynamics but also the unknown derivatives of virtual controllers in the controller design procedure, which can therefore prevent virtual controllers from containing uncertain terms. The projection algorithm is applied to ensure that the estimated parameters remain in some known bounded sets. Lyapunov stability analysis shows that the proposed control law can guarantee that the output of each agent synchronises to the leader with bounded residual errors and that all the signals in the closed-loop system are uniformly ultimately bounded. Simulation results have verified the performance and feasibility of the proposed distributed adaptive control strategy.     

Robust consensus algorithm for second-order multi-agent systems with external disturbances

This article investigates the problem of robust consensus for second-order multi-agent systems with external disturbances. Based on a non-smooth backstepping control technique, a class of novel continuous non-smooth consensus algorithms are proposed for the multi-agent network with/without communication delays. The controller design is divided into two steps. First, for the kinematic subsystem, the velocity is regarded as a virtual input and designed such that the states consensus can be achieved asymptotically. Then for the dynamic subsystem, a finite-time control law is designed such that the virtual velocity can be tracked by the real velocity in a finite time. Under the proposed control law, it is shown that if the communication topology graph contains a directed spanning tree, the states consensus can be achieved asymptotically in the absence of disturbances. In the presence of disturbances, the steady-state errors of any two agents can reach a small region around the origin. By building a relationship between control parameters and the bound of steady tracking errors, it is demonstrated that the disturbance rejection performance of the resulting closed-loop system can be enhanced by adjusting the fractional power in the non-smooth controller. Finally, an example is given to verify the efficiency of the proposed method.     

马尔可夫跳变系统基于观测器的有限时间容错控制

针对具有一般不确定转移速率的单边Lipschitz Markovian跳变系统,设计了有限时间故障估计观测器和容错控制器.首先,提出一种自适应的有限时间故障估计观测器,它对未知输入具有鲁棒性,能够同时估计出系统的状态、执行器故障和传感器故障,并确保了误差系统的H_∞有限时间有界.然后,基于所估计的状态和执行器故障,提出一种有限时间故障容错控制方法确保闭环系统H_∞有限时间有界.通过线性矩阵不等式的形式,给出了所设计的有限时间观测器和控制器存在的充分条件.最后,通过一个仿真实例,验证了所提方法的有效性.     

非线性不确定系统的非奇异快速终端滑模控制

针对存在非匹配干扰的非线性系统,设计了一种基于干扰观测器和反步法的非奇异快速终端滑模控制.引入非线性干扰观测器估计系统的不确定性,利用反步的思想处理高阶非线性系统,从而可以将非线性干扰观测器估计的干扰值引入反步法的虚拟控制量中,同时设计一种新颖的非奇异快速终端滑模控制律保证系统的收敛速度和精度.利用Lyapunov函数从理论上证明了所设计的控制器可以保证闭环系统的有限时间收敛.最后通过数值仿真验证了所设计的控制方法的有效性.     

基于虚拟结构法的分布式多无人机鲁棒编队控制

针对多无人机编队控制(UAVs)问题, 本文提出了一种基于虚拟结构法的非线性鲁棒控制算法. 首先将编队 控制问题转化成两个子问题: 在惯性坐标系下虚拟刚体(VRB)光滑轨迹的生成设计, 以及在虚拟刚体坐标系下的无 人机编队队形控制设计. 针对部分无人机无法直接获取虚拟刚体状态的约束, 通过引入相邻无人机的跟踪状态, 实 现了分布式的编队控制. 同时, 考虑多无人机近距离编队飞行时相互间的气流扰动影响, 设计了基于supertwisting 的鲁棒控制算法, 提高了编队系统的控制精度和稳定性. 利用Lyapunov稳定性分析方法, 证明了位置跟踪误差在 有限时间内收敛到滑模面, 得到闭环系统全局渐近稳定的结果. 最后通过实际飞行实验, 验证了所提控制算法的有 效性和鲁棒性.     

高超声速飞行器非线性鲁棒控制律设计

高超声速飞行器具有模型非线性程度高、耦合程度强、参数不确定性大、抗干扰能力弱等特点,其自主控制具有较大的挑战.论文提出了一种基于鲁棒补偿技术和反馈线性化方法的非线性鲁棒控制方法.文中首先采用反馈线性化的方法对纵向模型进行输入输出线性化,实现速度和高度通道的解耦和非线性模型的线性化.针对得到的线性模型,设计包括标称控制器和鲁棒补偿器的线性控制器.基于极点配置原理,设计标称控制器使标称线性系统具有期望的输入输出特性,利用鲁棒补偿器来抑制参数不确定性和外界扰动对于闭环控制系统的影响.基于小增益定理,证明了闭环控制系统的鲁棒稳定性和鲁棒跟踪性能.相比于非线性回路成形控制方法,仿真结果表明了所设计非线性鲁棒控制算法的有效性和优越性.     

飞行模拟转台非线性干扰观测器反步滑模控制器设计

本文针对考虑不确定性的飞行模拟转台伺服系统,提出了一种基于非线性干扰观测器的反步全局滑模补偿控制方法。该方法采用反步控制方法设计转速期望虚拟控制,然后利用非线性干扰观测器观测系统不确定干扰,进而对引入非线性干扰观测器的系统设计自适应全局滑模控制器,实现了飞行模拟转台伺服系统期望转角信号的鲁棒跟踪控制,仿真结果表明,该方法控制效果良好,具有很好的工程应用价值。