Previous Articles     Next Articles

Trajectory Tracking Control of Euler-Lagrange Systems with ISS-Like Robustness to Actuator Noises

WU Haiwen1, XU Dabo2   

  1. 1. School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China;
    Engineering and Technology Institute Groningen, Faculty of Science and Engineering, University of Groningen, Groningen 9747 AG, The Netherlands;
    2. Shien-Ming Wu School of Intelligent Engineering, South China University of Technology, Guangzhou 511442, China
  • Received:2020-09-13 Revised:2021-06-02 Online:2022-10-25 Published:2022-10-12
  • Supported by:
    This paper was supported in part by the National Natural Science Foundation of China under Grant Nos.61673216 and 62073168;The work of Wu was supported by the China Scholarship Council on his study at the University of Groningen,The Netherlands;The work of Xu was partially done when he was with the School of Automation,Nanjing University of Science and Technology,Nanjing 210094,China.

WU Haiwen, XU Dabo. Trajectory Tracking Control of Euler-Lagrange Systems with ISS-Like Robustness to Actuator Noises[J]. Journal of Systems Science and Complexity, 2022, 35(5): 1719-1747.

This paper studies global robust tracking of uncertain Euler-Lagrange systems with input disturbances.The authors develop a robust regulation-based approach for the problem.Specifically,by introducing a novel nonlinear internal model,the authors solve global asymptotic trajectory tracking with disturbance rejection of multiple step/sinusoidal signals with unknown amplitudes,frequencies,and phases.Moreover,the authors show that a robustness property to actuator noises can be guaranteed in a sense of strong integral input-to-state stability (iISS).That is,the closed-loop system is not only iISS but also input-to-state stable (ISS) to small magnitude actuator noises.Furthermore,the authors explore a by-product overparametrized linear regression estimation,coming up with robust estimation of the unknown parameters.Finally,the authors present several numerical examples to illustrate the theoretical results.
[1] Ortega R, Loría A, Nicklasson P J, et al., Passivity-Based Control of Euler-Lagrange Systems:Mechanical, Electrical and Electromechanical Applications, Springer Science&Business Media, Berlin, 1998.
[2] Slotine J J E and Li W, Applied Nonlinear Control, Prentice Hall, Englewood Cliffs, NJ, 1991.
[3] Spong M W, Hutchinson S, and Vidyasagar M, Robot Modeling and Control, Wiley, New York, 2006.
[4] Craig J J, Hsu P, and Sastry S S, Adaptive control of mechanical manipulators, The International Journal of Robotics Research, 1987, 6(2):16-28.
[5] Middleton R H and Goodwin G C, Adaptive computed torque control for rigid link manipulations, Systems&Control Letters, 1988, 10(1):9-16.
[6] Spong M W and Ortega R, On adaptive inverse dynamics control of rigid robots, IEEE Transactions on Automatic Control, 1990, 35(1):92-95.
[7] Dawson D M and Lewis F L, Comments on "On adaptive inverse dynamics control of rigid robots", IEEE Transactions on Automatic Control, 1991, 36(10):1215-1216.
[8] Slotine J J E and Li W, On the adaptive control of robot manipulators, The International Journal of Robotics Research, 1987, 6(3):49-59.
[9] Slotine J J E, Putting physics in control-The example of robotics, IEEE Control Systems Magazine, 1988, 8(6):12-18.
[10] Leal R L and Dewit C C, Passivity based adaptive control for mechanical manipulators using LS-type estimation, IEEE Transactions on Automatic Control, 1990, 35(12):1363-1365.
[11] Tang Y and Arteaga M A, Adaptive control of robot manipulators based on passivity, IEEE Transactions on Automatic Control, 1994, 39(9):1871-1875.
[12] Scherpen J M A and Ortega R, On nonlinear control of Euler-Lagrange systems:Disturbance attenuation properties, Systems&Control Letters, 1997, 30(1):49-56.
[13] Tomei P, Tracking control of flexible joint robots with uncertain parameters and disturbances, IEEE Transactions on Automatic Control, 1994, 39(5):1067-1072.
[14] Luo G L and Saridis G N, Robust compensation for a robotic manipulator, IEEE Transactions on Automatic Control, 1983, 29(6):564-567.
[15] Chen B S, Lee T S, and Feng J H, A nonlinear H∞ control design in robotic systems under parameter perturbation and external disturbance, International Journal of Control, 1994, 59(2):439-461.
[16] Battilotti S and Lanari L, Adaptive disturbance attenuation with global stability for rigid and elastic joint robots, Automatica, 1997, 33(2):239-243.
[17] Tomei P, Robust adaptive control of robots with arbitrary transient performance and disturbance attenuation, IEEE Transactions on Automatic Control, 1999, 44(3):654-658.
[18] Mei K, Ding S, Yang X, et al., Second-order sliding mode controller design with a larger domain of attraction, Journal of Systems Science&Complexity, 2020, 33(1):61-73.
[19] Patre P M, MacKunis W, Dupree K, et al., Modular adaptive control of uncertain Euler-Lagrange systems with additive disturbances, IEEE Transactions on Automatic Control, 2011, 56(1):155-160.
[20] Chen B S, Chang Y C, and Lee T C, Adaptive control in robotic systems with H∞ tracking performance, Automatica, 1997, 33(2):227-234.
[21] Jayawardhana B and Weiss G, Tracking and disturbance rejection for fully actuated mechanical systems, Automatica, 2008, 44(11):2863-2868.
[22] Lu M, Liu L, and Feng G, Adaptive tracking control of uncertain Euler-Lagrange systems subject to external disturbances, Automatica, 2019, 104:207-219.
[23] Wu H and Xu D, Inverse optimality and adaptive asymptotic tracking control of uncertain Euler-Lagrange systems, 2019 IEEE 15th International Conference on Control and Automation (ICCA), 2019, 242-247.
[24] Sontag E D, Input to state stability:Basic concepts and results, Eds. by Nistri P and Stefani G, Nonlinear and Optimal Control Theory, Springer, Berlin, 2007, 163-220.
[25] Angeli D, Input-to-state stability of PD-controlled robotic systems, Automatica, 1999, 35(7):1285-1290.
[26] Angeli D, Sontag E D, and Wang Y, A characterization of integral input-to-state stability, IEEE Transactions on Automatic Control, 2000, 45(6):1082-1097.
[27] Liberzon D, Sontag E D, and Wang Y, Universal construction of feedback laws achieving ISS and integral-ISS disturbance attenuation, Systems&Control Letters, 2002, 46(2):111-127.
[28] Jiang Z P and Hill D J, Passivity and disturbance attenuation via output feedback for uncertain nonlinear systems, IEEE Transactions on Automatic Control, 1998, 43(7):992-997.
[29] Liu T, Jiang Z P, and Hill D J, Nonlinear Control of Dynamic Networks, CRC Press, New York, 2014.
[30] Huang J and Chen Z, A general framework for tackling the output regulation problem, IEEE Transactions on Automatic Control, 2004, 49(12):2203-2218.
[31] Xu D, Constructive nonlinear internal models for global robust output regulation and application, IEEE Transactions on Automatic Control, 2018, 63(5):1523-1530.
[32] Xu D and Huang J, A generic internal model for robust output regulation problem for plants subject to an uncertain exosystem, 2019 IEEE 15th International Conference on Control and Automation (ICCA), 2019, 1179-1184.
[33] Chaillet A, Angeli D, and Ito H, Combining iISS and ISS with respect to small inputs:The strong iISS property, IEEE Transactions on Automatic Control, 2014, 59(9):2518-2524.
[34] Huang J, Nonlinear Output Regulation:Theory and Applications, SIAM, Philadelphia, 2004.
[35] Byrnes C I and Isidori A, Limit sets, zero dynamics, and internal models in the problem of nonlinear output regulation, IEEE Transactions on Automatic Control, 2003, 48(10):1712-1723.
[36] Bastin G, Bitmead R R, Campion G, et al. Identification of linearly overparametrized nonlinear systems, IEEE Transactions on Automatic Control, 1992, 37(7):1073-1078.
[37] Sun W, Xia J, and Wu Y, Adaptive tracking control for mobile manipulators with stochastic disturbances, Journal of Systems Science&Complexity, 2019, 32(5):1393-1403.
[38] Byrnes C I and Isidori A, Nonlinear internal models for output regulation. IEEE Transactions on Automatic Control, 2004, 49(12):2244-2247.
[39] Krstić M, Kanellakopoulos I, and Kokotović P V, Nonlinear and Adaptive Control Design, Wiley, New York, 1995.
[40] Astolfi D, Isidori A, Marconi L, et al., Nonlinear output regulation by post-processing internal model for multi-input multi-output systems, IFAC Proceedings Volumes, 2013, 46(23):295-300.
[41] Bin M and Marconi L, Output regulation by postprocessing internal models for a class of multivariable nonlinear systems, International Journal of Robust and Nonlinear Control, 2020, 30(3):1115-1140.
[42] Xu D, Chen Z, and Wang X, Global robust stabilization of nonlinear cascaded systems with integral ISS dynamic uncertainties, Automatica, 2017, 80:210-217.
[43] Wang H and Xie Y, Flocking of networked mechanical systems on directed topologies:A new perspective, International Journal of Control, 2015, 88(4):872-884.
[44] Sontag E D and Wang Y, New characterizations of input-to-state stability, IEEE Transactions on Automatic Control, 1996, 41(9):1283-1294.
[45] Xu D, Wang X, and Chen Z, Output regulation of nonlinear output feedback systems with exponential parameter convergence, Systems&Control Letters, 2016, 88:81-90.
[46] Zhang Y and Guo L, Convergence of self-tuning regulators under conditional heteroscedastic noises with unknown high-frequency gain, Journal of Systems Science&Complexity, 2021, 34(1):236-250.
[47] Sastry S, Nonlinear Systems:Analysis, Stability and Control, Springer-Verlag, New York, NY, USA, 1999.
[48] Khalil H K, Nonlinear Systems, Prentice Hall, New Jersey, 2002.
[1] CHEN Zhixiang. Active Disturbance Rejection Control of Second-Order Nonlinear Uncertain Systems with Guaranteed Transient and Steady State Tracking Error Bounds [J]. Journal of Systems Science and Complexity, 2022, 35(4): 1293-1309.
[2] KONG Xiangyu, XIA Yuanqing, HU Rui, LIN Min, SUN Zhongqi, DAI Li. Trajectory Tracking Control for Under-Actuated Hovercraft Using Differential Flatness and Reinforcement Learning-Based Active Disturbance Rejection Control [J]. Journal of Systems Science and Complexity, 2022, 35(2): 502-521.
[3] SUN Hao, HUANG Ling, HE Liang. Research on the Trajectory Tracking Control of a 6-DOF Manipulator Based on Fully-Actuated System Models [J]. Journal of Systems Science and Complexity, 2022, 35(2): 641-659.
[4] GUO Wei,SHAO Zhi-Chao. Backstepping Approach to the Adaptive Regulator Design for a One-Dimensional Wave Equation with General Input Harmonic Disturbance [J]. Journal of Systems Science and Complexity, 2017, 30(2): 253-279.
[5] XUE Wenchao,HUANG Yi. Tuning of Sampled-Data ADRC for Nonlinear Uncertain Systems [J]. Journal of Systems Science and Complexity, 2016, 29(5): 1187-1211.
[6] GUO Jianxin,XUE Wenchao,HU Tao. Active Disturbance Rejection Control for PMLM Servo System in CNC Machining [J]. Journal of Systems Science and Complexity, 2016, 29(1): 74-98.
[7] HE Yudong,WANG Junzheng,HAO Renjian. Adaptive Robust Dead-Zone Compensation Control of Electro-Hydraulic Servo Systems with Load Disturbance Rejection [J]. Journal of Systems Science and Complexity, 2015, 28(2): 341-359.
[8] Bin ZHOU;Guangren DUAN;He KONG. GLOBAL STABILIZATION OF LINEAR SYSTEMS WITH BOUNDEDCONTROLS USING STATE-DEPENDENT SATURATION FUNCTIONS [J]. Journal of Systems Science and Complexity, 2011, 24(3): 477-490.
[9] Teddy M. CHENG. ROBUST OUTPUT FEEDBACK STABILIZATION OF NONLINEAR NETWORKED SYSTEMS VIA A FINITE DATA-RATE COMMUNICATION CHANNEL [J]. Journal of Systems Science and Complexity, 2011, 24(1): 1-013.
[10] Xiaohua LIU;Chunyan HAN. ROBUST MODEL PREDICTIVE CONTROL OF CONTINUOUS UNCERTAIN SYSTEMS [J]. Journal of Systems Science and Complexity, 2008, 21(2): 267-275.
[11] Jian Feng WEI;Yu Fan ZHANG. A NOTE ON NONLINEAR ROBUST H_∞ ALMOST DISTURBANCE DECOUPLING PROBLEM WITH STABILITY [J]. Journal of Systems Science and Complexity, 2002, 15(1): 35-042.
[12] Yi HUANG;Jing Qing HAN. DISTURBANCE REJECTION AND TRACKING DESIGN VIA THE SSR APPROACH FOR SECOND ORDER UNCERTAIN SYSTEMS [J]. Journal of Systems Science and Complexity, 1999, 12(Supplement): 96-103.
[13] WANG Enping. ROBUST STABILIZATION OF SYSTEM WITHNUMERATORAL FACTOR PERTURBATION [J]. Journal of Systems Science and Complexity, 1998, 11(2): 184-192.
[14] YUAN Zhendong;CHEN Qi;DING Sheng;DIAO Lianwang. CREDIBLE SETS FOR SYSTEM PARAMETERS AND TRANSFER FUNCTIONS [J]. Journal of Systems Science and Complexity, 1998, 11(2): 150-160.
[15] ZHENG Yufan;CAO Li. THE RANKINGS OF CONTROL SYSTEMS AND APPLICATIONS [J]. Journal of Systems Science and Complexity, 1993, 6(3): 231-238.
Viewed
Full text


Abstract