Adaptive CFB Control for a Class of Nonlinear Systems With Intermittent Actuator Faults
-
摘要: 控制系统的执行器经常发生各种未知的间歇性故障. 如何有效地处理这些故障对系统的影响是一个难题. 针对一类不确定严格反馈非线性系统, 提出一种自适应CFB (Command filtered backstepping) 控制方案解决了间歇性执行器故障的补偿问题. 利用神经网络逼近控制器中的未知函数, 并采用投影算子实时在线更新控制器中的估计参数使得参数估计值随着故障次数的累积而不断增加的问题被消除. 提出改进的Lyapunov函数证明了所提出的方案能够保证所有闭环信号的有界性, 同时建立了跟踪误差与Lyapunov函数跳变幅度, 最小故障时间间隔, 设计参数之间的关系. 如果Lyapunov函数的跳变幅度越小以及两个连续故障之间的时间间隔越长, 系统的稳态跟踪指标越好. 通过迭代计算建立了暂态跟踪误差指标的均方根型界. 该界表明了通过选择恰当的设计参数, 可改善系统的暂态指标. 仿真结果表明了所提方案的有效性.Abstract: Actuators of control systems frequently encounter various unknown intermittent faults. How to effectively handle the effects of such faults on the system is a difficult problem. In this paper, an adaptive command filtered backstepping (CFB) compensation control scheme is proposed for a class of uncertain strict-feedback nonlinear systems to address the issue of compensation for intermittent actuator faults. Neural networks are utilized in the controller to approximate unknown functions, and a smooth projection algorithm is adopted to update the estimated parameters in the controller such that the problem of parameter estimate increase with the accumulation of the number of faults is eliminated. A modified Lyapunov function is developed to prove that the proposed scheme can guarantee the boundedness of all closed-loop signals and, the relationship among the tracking error, jumping amplitude of Lyapunov function, minimum fault time interval and design parameters can be established. It is shown that if the jumping amplitude of Lyapunov function is smaller and the time interval between two adjacent faults is longer, the system steady-state tracking performance is better. A root mean square type of bound for the transient tracking error performance is established by using iterative calculation to illustrate that the system transient performance is improved by appropriate choice of design parameters. Simulation results validate the effectiveness of the proposed scheme.
-
图 1 控制结构图 (
$x_{\mathrm{c}i}$ 和$\dot{x}_{\mathrm{c}i}$ ,$i = 2,\cdots,n$ , 为滤波器 (11) 的输出.$\alpha_i$ ,$i = 1,\cdots,n$ , 为式 (12) ~ (14) 中定义的虚拟控制律.$\xi_i$ ,$i = 1,\cdots,n-1$ 为式 (17) 中定义的滤波误差补偿信号)Fig. 1 Control block diagram (
$x_{\mathrm{c}i}$ and$\dot{x}_{\mathrm{c}i}$ for$i = $ $ 2, \cdots,n$ are the outputs of the filter (11).$\alpha_i$ for$i = $ $ 1,\cdots,n$ is virtual control law defined in (12) ~ (14).$\xi_i$ for$i = 1,\cdots, $ $ n-1$ is the compensating signal of the filtered error defined in (17))
图 2 实验1中输出
$y $ , 期望轨迹$y_{\mathrm{d}} $ 及跟踪误差$\bar{z}_1 $ Fig. 2 Output
$y $ , desired trajectory$y_{\mathrm{d}} $ and tracking error$\bar{z}_1 $ in Experiment 1
图 4 实验1中命令滤波误差及其补偿信号
Fig. 4 Command filtered errors and their compensating signals in Experiment 1
图 6 实验2中输出
$y $ , 期望轨迹$y_{\mathrm{d}} $ 及跟踪误差$\bar{z}_1 $ Fig. 6 Output
$y $ , desired trajectory$y_{\mathrm{d}} $ and tracking error$\bar{z}_1 $ in Experiment 2
图 8 实验2中命令滤波误差及其补偿信号
Fig. 8 Command filtered errors and their compensating signals in Experiment 2
图 10 实验3中输出
$y $ , 期望轨迹$y_{\mathrm{d}} $ 及跟踪误差$\bar{z}_1 $ Fig. 10 Output
$y $ , desired trajectory$y_{\mathrm{d}} $ and tracking error$\bar{z}_1 $ in Experiment 3
图 12 实验3中命令滤波误差及其补偿信号
Fig. 12 Command filtered errors and their compensating signals in Experiment 3
图 14 实验4中输出
$y $ , 期望轨迹$y_{\mathrm{d}} $ 及跟踪误差$\bar{z}_1 $ Fig. 14 Output
$y $ , desired trajectory$y_{\mathrm{d}} $ and tracking error$\bar{z}_1 $ in Experiment 4
图 16 实验4中命令滤波误差及其补偿信号
Fig. 16 Command filtered errors and their compensating signals in Experiment 4
-
[1] Tao G, Chen S, Tang X, Joshi S. M. Adaptive control of systems with actuator failures. Springer Science and Business Media, 2013. [2] Ahmed-Zaid F, Ioannou P, Gousman K, et al. Accommodation of failures in the F-16 aircraft using adaptive control. IEEE Control Systems Magazine, 1991, 11(1): 73−78. doi: 10.1109/37.103360 [3] Bodson M, Groszkiewicz J E. Multivariable adaptive algorithms for reconfigurable flight control. IEEE Transactions on Control Systems Technology, 1997, 5(2): 217−229. doi: 10.1109/87.556026 [4] Ye D, Yang G H. Adaptive fault-tolerant tracking control against actuator faults with application to flight control. IEEE Transactions on Control Systems Technology, 2006, 14(6): 1088−1096. doi: 10.1109/TCST.2006.883191 [5] Yang G H, Ye D. Reliable ${{\cal H}_\infty }$ control of linear systems with adaptive mechanism. IEEE Transactions on Automatic Control, 2009, 55(1): 242−247.[6] 金小峥, 杨光红, 常晓恒, 车伟伟. 容错控制系统鲁棒 ${{\cal H}_\infty }$ 和自适应补偿设计. 自动化学报, 2013, 39(1): 31−42 doi: 10.1016/S1874-1029(13)60004-XJin Xiao-Zheng, Yang Guang-Hong, Chang Xiao-Heng, Che Wei-Wei. Robust fault-tolerant${{\cal H}_\infty }$ control with adaptive compensation. Acta Automatica Sinica, Acta Automatica Sinica, 39(1): 31−42. doi: 10.1016/S1874-1029(13)60004-X[7] Tao G, Joshi S M, Ma X. Adaptive state feedback and tracking control of systems with actuator failures. IEEE Transactions on Automatic Control, 2001, 46(1): 78−95. doi: 10.1109/9.898697 [8] Xu B, Guo Y, Yuan Y, Fan Y, Wang D. Fault-tolerant control using command-filtered adaptive backstepping technique: Application to hypersonic longitudinal flight dynamics. International Journal of Adaptive and Control Signal Processing., 2016, 30(4): 553−577. doi: 10.1002/acs.2596 [9] Tang X, Tao G, Joshi S M. Adaptive actuator failure compensation for parametric strict feedback systems and an aircraft application. Automatica, 2003, 39(11): 1975−1982. doi: 10.1016/S0005-1098(03)00219-X [10] Tang X, Tao G, Joshi S M. Adaptive actuator failure compensation for nonlinear MIMO systems with an aircraft control application. Automatica, 2007, 43(11): 1869−1883. doi: 10.1016/j.automatica.2007.03.019 [11] Wang W, Wen C. Adaptive actuator failure compensation control of uncertain nonlinear systems with guaranteed transient performance. Automatica, 2010, 46(12): 2082−2091. doi: 10.1016/j.automatica.2010.09.006 [12] Zhai D, An L, Li J, Zhang Q. Adaptive fuzzy fault-tolerant control with guaranteed tracking performance for nonlinear strict-feedback systems. Fuzzy Sets and Systems, 2016, 302: 82−100. doi: 10.1016/j.fss.2015.10.006 [13] Chakravarty A, Nizami T K, Kar I, Mahanta C. Adaptive Compensation of Actuator Failures using Multiple Models. IFAC-PapersOnLine, 2017, 50(1): 10350−10356. doi: 10.1016/j.ifacol.2017.08.1681 [14] Li Y X, Yang G H. Fuzzy adaptive output feedback faulttolerant tracking control of a class of uncertain nonlinear systems with nonaffine nonlinear faults. IEEE Transactions on Fuzzy Systems, 2016, 24(1): 223−234. doi: 10.1109/TFUZZ.2015.2452940 [15] Li Y, Sun K, Tong S. Observer-based adaptive fuzzy faulttolerant optimal control for SISO nonlinear systems. IEEE Transactions on Cybernetics, 2019, 49(2): 649−661. doi: 10.1109/TCYB.2017.2785801 [16] Wu C, Liu J, Xiong Y, Wu L. Observer-based adaptive faulttolerant tracking control of nonlinear nonstrict-feedback systems. IEEE Transactions on Neural Networks and Learning systems, 2017, 29(7): 3022−3033. [17] Zhao K, Song Y, Shen Z. Neuroadaptive fault-tolerant control of nonlinear systems under output constraints and actuation faults. IEEE Transactions on Neural Networks and Learning systems, 2016, 29(2): 286−298. [18] Liu L, Liu Y J, Tong S. Neural networks-based adaptive finite-time fault-tolerant control for a class of strict-feedback switched nonlinear systems. IEEE Transactions on Cybernetics, 2019, 49(7): 2536−2545. doi: 10.1109/TCYB.2018.2828308 [19] 张绍杰, 吴雪, 刘春生. 执行器故障不确定非线性系统最优自适应输出跟踪控制. 自动化学报, 2018, 44(12): 2188−2197Zhang Shao-Jie, Wu Xue, Liu Chun-Sheng. Optimal adaptive output tracking control for a class of uncertain nonlinear systems with actuator failures. Acta Automatica Sinica, 2018, 44(12): 2188−2197. [20] Wang W, Wen C. Adaptive compensation for infinite number of actuator failures or faults. Automatica, 2011, 47(10): 2197−2210. doi: 10.1016/j.automatica.2011.08.022 [21] Lai G, Liu Z, Chen C L P, Zhang Y, Chen X. Adaptive compensation for infinite number of time-varying actuator failures in fuzzy tracking control of uncertain nonlinear systems. IEEE Transactions on Fuzzy Systems, 2018, 26(2): 474−486. doi: 10.1109/TFUZZ.2017.2686338 [22] Lai G, Wen C, Liu Z, Zhang Y, Chen C P, Xie S. Adaptive compensation for infinite number of actuator failures based on tuning function approach. Automatica, 2018, 87: 365−374. doi: 10.1016/j.automatica.2017.07.014 [23] Xing L, Wen C, Liu Z, Su H, Cai J. Adaptive compensation for actuator failures with event-triggered input. Automatica, 2017, 85: 129−136. doi: 10.1016/j.automatica.2017.07.061 [24] Jing Y H, Yang G H. Neural-network-based adaptive faulttolerant tracking control of uncertain nonlinear time-delay systems under output constraints and infinite number of actuator faults. Neurocomputing, 2018, 272: 343−355. doi: 10.1016/j.neucom.2017.07.009 [25] Yang H, Jiang B, Zhang Y. Tolerance of intermittent faults in spacecraft attitude control: switched system approach. IET Control Theory & Applications, 2012, 6(13): 2049−2056. [26] Krstic M, Kanellakopoulos I, Kokotovic V. Nonlinear and Adaptive Control Design. New York: Wiley, 1995. [27] Wen C, Zhou J. Decentralized adaptive stabilization in the presence of unknown backlash-like hysteresis. Automatica, 2007, 43(3): 426−440. doi: 10.1016/j.automatica.2006.10.012 [28] Wang C, Wen C, Lin Y. Adaptive actuator failure compensation for a class of nonlinear systems with unknown control direction. IEEE Transactions on Automatic Control, 2016, 62(1): 385−392. [29] Lai G, Wen C, Liu Z, Zhang Y, Chen C P, Xie S. Adaptive compensation for infinite number of actuator failures/faults using output feedback control. Information Sciences, 2017, 399: 1−12. doi: 10.1016/j.ins.2017.02.022 [30] Dong W, Farrell J A, Polycarpou M M, et al. Command filtered adaptive backstepping. IEEE Transactions on Control Systems Technology, 2012, 20(3): 566−580. doi: 10.1109/TCST.2011.2121907 [31] Zhao Y, Farrell J A. Localized adaptive bounds for approximation-based backstepping. Automatica, 2008, 44(10): 2607−2613. doi: 10.1016/j.automatica.2008.02.013 [32] Khalil H K. Nonlinear Systems (3rd Edition). NJ: Prentice-Hall, 2002. [33] Huang G B, Zhu Q Y, Siew C K. Extreme learning machine: theory and applications. Neurocomputing, 2006, 70(1-3): 489−501. doi: 10.1016/j.neucom.2005.12.126 [34] Huang G B, Chen L, Siew C K. Universal approximation using incremental constructive feedforward networks with random hidden nodes. IEEE Transactions on Neural Networks, 2006, 17(4): 879−892. doi: 10.1109/TNN.2006.875977 [35] Pomet J B, Praly L. Adaptive nonlinear regulation: Estimation from the Lyapunov equation. IEEE Transactions on Automatic Control, 1992, 37(6): 729−740. doi: 10.1109/9.256328 [36] Yang Y, Feng G, Ren J. A combined backstepping and smallgain approach to robust adaptive fuzzy control for strictfeedback nonlinear systems. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 2004, 34(3): 406−420. doi: 10.1109/TSMCA.2004.824870 -
下载:
计量
- 文章访问数: 1091
- HTML全文浏览量: 388
- PDF下载量: 377
- 被引次数: 0
