Reduction of matched and unmatched uncertainties for a class of nonlinear perturbed systems via robust control

The aim of this paper is to design a robust control for stabilization of a class of nonlinear perturbed system subject to matched and unmatched disturbances. Here, the concept of dynamic sliding mode control and the attractive ellipsoid method advantages are used to design a robust nonlinear control algorithm, which reduces considerably the perturbation effects. Hence, in finite time, the dynamic sliding mode control brings the system trajectory to a specific configuration. After this time, the controller reduces the perturbation effects by using the high‐gain control obtained in the attractive ellipsoid method. Thus, based on the solution of a specific matrix inequality, the feedback control of the system guarantees that the trajectory will be stabilized in the ultimate uniform bounded sense. To illustrate the theoretical results, a numerical example with a comparative study is introduced. Finally, the performance of the controller designed in this paper is tested on an electromechanical real‐time system.     

An adaptive critic approach to event‐triggered robust control of nonlinear systems with unmatched uncertainties

In this paper, we develop a novel event‐triggered robust control strategy for continuous‐time nonlinear systems with unmatched uncertainties. First, we build a relationship to show that the event‐triggered robust control can be obtained by solving an event‐triggered nonlinear optimal control problem of the auxiliary system. Then, within the framework of reinforcement learning, we propose an adaptive critic approach to solve the event‐triggered nonlinear optimal control problem. Unlike typical actor‐critic dual approximators used in reinforcement learning, we employ a unique critic approximator to derive the solution of the event‐triggered Hamilton‐Jacobi‐Bellman equation arising in the nonlinear optimal control problem. The critic approximator is updated via the gradient descent method, and the persistence of excitation condition is necessary. Meanwhile, under a newly proposed event‐triggering condition, we prove that the developed critic approximator update rule guarantees all signals in the auxiliary closed‐loop system to be uniformly ultimately bounded. Moreover, we demonstrate that the obtained event‐triggered optimal control can ensure the original system to be stable in the sense of uniform ultimate boundedness. Finally, a F‐16 aircraft plant and a nonlinear system are provided to validate the present event‐triggered robust control scheme.     

非匹配不确定离散系统的无抖振积分滑模控制

针对一类非匹配不确定离散系统, 设计一种无抖振离散积分滑模控制器. 为了抑制非匹配不确定性对系统的影响, 采用线性矩阵不等式方法设计一种新型的切换函数和对应的滑模控制律, 并证明了闭环系统的Lyapunov 稳定性. 同时, 引入饱和函数设计控制器, 使系统状态在积分滑模面的某个小邻域内做准滑模运动, 并通过合理选择饱和函数的边界层厚度, 使控制信号不含任何抖振. 理论分析和数值仿真验证了所提出方法的有效性.

     

一类非匹配不确定性非线性系统的鲁棒镇定

研究了非线性系统存在非匹配不确定性时控制器的鲁棒镇定问题. 基于对象的模糊动态模型, 提出了一种状态反馈控制器的设计, 给出控制器在建模不确定性等各种非匹配不确定性存在下仍能够镇定非线性系统的一个充分条件. 仿真结果表明了设计方法的正确性.     

Interval observer framework for fault-tolerant control of linear parameter-varying systems

This paper addresses the problem of passive fault-tolerant control for linear parameter-varying systems subject to actuator faults. The FTC, based on a linear state feedback, is designed to compensate the impact of actuator faults on system performance by stabilising the closed-loop system using interval observers. The design of interval observers is based on the discrete-time Luenberger observer structure, where uncertainties and faults with known bounds are considered. Sufficient conditions for the existence of the proposed observer are explicitly provided. Simulation results are presented to show the effectiveness of the proposed approach.     

带有非线性不确定奇异系统的积分滑模控制

针对一类含有非线性不确定的奇异系统, 提出了一种面向性能的鲁棒控制器. 控制器由3部分组成: 积分滑模控制、附加的非线性控制及复合非线性反馈控制. 积分滑模控制可将匹配不确定完全抵消并使系统轨迹进入理想滑模; 附加的非线性控制用来抑制理想滑动模态上非匹配不确定对系统稳定性和性能的影响; 复合非线性反馈控制则保证闭环系统输出按性能要求渐近地跟踪参考输入信号. 最后通过算例说明所提算法的有效性.     

非匹配不确定M I MO 线性系统的终端滑模控制

提出一种用于非匹配不确定MIMO线性系统的终墙滑模控制方法。设计了特殊的终墙滑模切换面和相应的控制策略，使得系统在有限时问内收敛到终墙滑模面，在系统到达终墙滑模面后保证系统的状态保持在终墙滑模面上，并在有限时闻内收敛到平衡点附近的邻域内，建立了谈邻域的范圈与系统的非匹配不确定性的范圈以及终蜡滑模参数之闻的数学关系，用于系统设计与分析，仿真结果验证了所提出方法的有效性和分析的正确性。     

Generation of stable oscillations in uncertain nonlinear systems with matched and unmatched uncertainties

ABSTRACT

In this paper, a robust limit cycle control technique is proposed for generation of stable oscillations in a class of uncertain nonlinear systems with both matched and unmatched uncertainties. For this purpose, first, the modified Lyapunov function is introduced which is appropriate for stability analysis of invariant sets (instead of equilibrium points). The structure of the proposed Lyapunov function is related to the shape of the desirable limit cycle. Next, in order to design the robust limit cycle control input, the backstepping and Lyapunov redesign methods are employed, simultaneously. The The classical Lyapunov redesign controller is discontinuous and robust with respect to matched uncertainties. To overcome unmatched uncertainties, a modified version of the Lyapunov redesign controller is suggested in each step of backstepping which results in a continuous robust control law. Furthermore, the convergence of the phase trajectories of the uncertain closed-loop system to the target limit cycle is proved using the extended Lyapunov stability theorem. Finally, computer simulations are performed to show the applicability of the given approach. In this regard, two uncertain nonlinear practical systems are considered and robust stable oscillations are generated in these systems via the proposed controller. Simulation results confirm the effectiveness of the proposed technique.     

不确定性机器人系统自适应鲁棒迭代学习控制

利用Lyapunov方法, 提出了一种不确定性机器人系统的自适应鲁棒迭代学习控制策略, 整个系统在迭代域里是全局渐近稳定的. 所考虑的机器人系统同时包含了结构和非结构不确定性. 在设计时, 系统的不确定性被分解成可重复性和非重复性两部分, 并考虑了系统的标称模型. 在所提出的控制策略中, 自适应策略用来估算做法确定性的界, 界的修正与迭代学习控制量一样的迭代域得以实现的. 计算机仿真表明本文提出的控制策略是有效的.     

Adaptive fault-tolerant control of linear systems with actuator saturation and L2-disturbances

This paper studies the problem of designing adaptive fault-tolerant H-infinity controllers for linear timeinvariant systems with actuator saturation. The disturbance tolerance ability of the closed-loop system is measured by an optimal index. The notion of an adaptive H-infinity performance index is proposed to describe the disturbance attenuation performances of closed-loop systems. New methods for designing indirect adaptive fault-tolerant controllers via state feedback are presented for actuator fault compensations. Based on the on-line estimation of eventual faults, the adaptive fault-tolerant controller parameters are updated automatically to compensate for the fault effects on systems. The designs are developed in the framework of the linear matrix inequality （LMI） approach, which can guarantee the disturbance tolerance ability and adaptive H-infinity performances of closed-loop systems in the cases of actuator saturation and actuator failures. An example is given to illustrate the efficiency of the design method.     

线性电机伺服系统的自适应鲁棒控制

通过对一类音圈电机直驱式精密伺服系统运动控制问题的研究,在只考虑系统标称模型的情况下,采用分数阶形式的趋近律,得到了一种有限时间滑模控制算法;与此同时,当系统存在参数不确定和外界干扰的情况下,将有限时间滑模控制方法和自适应控制理论相结合,构造了一种自适应滑模控制律.另一方面,本文还考虑了系统具有输入饱和约束的情况,通过引入一个辅助系统,进而设计了一种自适应抗饱和控制律.而且,文中对闭环系统的稳定性进行了证明.最后,仿真和实验对所提出控制策略的有效性和伺服精度进行了对比、分析和验证.     

Adaptive fault-tolerant control of linear time-invariant systems in the presence of actuator saturation

This paper studies the problem of designing adaptive fault-tolerant controllers for linear tirne-invariant systems with actuator saturation. New methods for designing indirect adaptive fault-tolerant controllers via state feedback are presented for actuator fault compensations. Based on the on-line estimation of eventual faults, the adaptive fault-tolerant controller parameters are updating automatically to compensate the fault effects on systems. The designs are developed in the framework of linear matrix inequality （LMI） approach, which can enlarge the domain of attraction of closed-loop systems in the cases of actuator saturation and actuator failures. Two examples are given to illustrate the effectiveness of the design method.     

一类非线性MIMO系统的直接自适应模糊鲁棒控制

针对一类未知的非线性MIMO系统, 本文提出了一种直接自适应模糊鲁棒控制设计方法. 理论分析和仿真实验都已证明, 该方法确保闭环系统全局稳定, 获得H_∞跟踪性能指标, 外部干扰、模糊逻辑逼近误差和输入对输出的交叉耦合可衰减到给定的水平, 系统鲁棒性好.     

Adaptive fault-tolerant control of linear systems with actuator saturation and L_2-disturbances

This paper studies the problem of designing adaptive fault-tolerant H-infinity controllers for linear timeinvariant systems with actuator saturation.The disturbance tolerance ability of the closed-loop system is measured by an optimal index.The notion of an adaptive H-infinity performance index is proposed to describe the disturbance attenuation performances of closed-loop systems.New methods for designing indirect adaptive fault-tolerant controllers via state feedback are presented for actuator fault compe...     

Adaptive quantised fault-tolerant tracking control of uncertain nonlinear systems with unknown control direction and the prescribed accuracy

In this paper, the problem of adaptive fault-tolerant tracking control for a class of uncertain nonlinear systems in the presence of input quantisation and unknown control direction is considered. By choosing a class of particular Nussbaum functions, an adaptive fault-tolerant control scheme is designed to compensate actuator faults and input quantisation while the control direction is unknown. Compared with the existing results, the proposed controller can directly compensate for the nonlinear term caused by actuator faults and the nonlinear decomposition on the quantiser without estimating its bound. Furthermore, via Barhalant's Lemma, it is proven that all the signals of the closed-loop system are globally uniformly bounded and the tracking error converges into a prescribed accuracy in prior. Finally, an illustrative example is used for verifying effectiveness of the proposed approach.     

具有未知上界时滞状态扰动的非线性系统自适应鲁棒镇定

讨论了一类具有时滞状态扰动的非线性系统的自适应鲁棒镇定问题.时滞状态扰动的上界是未知的.在控制中通过自适应律估计上界的值,并且利用估计值设计鲁棒控制器.基于Lyapunov-Krasovskii函数,证明了闭环系统具有一致最终有界意义下的鲁棒稳定性.最后通过一个数值例子的仿真验证了结论的正确性.     

非匹配离散系统无抖振鲁棒准滑模控制

研究离散准滑动模态的鲁棒性恢复和抖振削弱问题。针对一类同时含有匹配建模误差和非匹配外界干扰不确定离散系统,设计一种基于解耦干扰补偿器的鲁棒准滑模控制方案。为保证系统的鲁棒性,针对非匹配外界干扰设计一种改进的解耦干扰补偿器,估计误差有界收敛。通过引入幂次函数设计鲁棒离散准滑模控制器,消除系统抖振,给出切换函数准滑模带,并证明了闭环系统离散准滑动模态的稳定可达性。最后通过仿真验证了所提出控制方案的有效性。     

不确定时滞系统的时滞依赖鲁棒非脆弱H∞控制

基于线性矩阵不等式(LMI)方法, 研究了不确定时滞线性系统的鲁棒非脆弱H_∞状态反馈控制器的设计问题, 以一个LMI形式给出了控制器存在的充分条件, 而且该LMI是与时滞相关的. 同时, 经过全等变换、变量变换和Schur补引理, 该LMI的所有参数都是线性的, 这样参数无需预取就可以利用LMI Toolbox获得解. 实例表明了上述设计方法的有效性.     

A robust adaptive dynamic surface control for linear systems

In this article, a robust output-feedback adaptive dynamic surface control (DSC) is proposed for linear time-invariant single-input single-output plants with unmodelled dynamics and unmeasurable output disturbance. With the proposed adaptive DSC scheme, the ‘explosion of terms’ problem inherent in backstepping control is eliminated and the adaptive law is necessary only at the first design step, which significantly reduces the design procedure. More importantly, it is proved that with an initialisation technique, the ?_∞ performance of the tracking error can be guaranteed even with unmodelled dynamics, bounded output disturbance exists and the plant high-frequency gain is unknown.     

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.