Authors

Chengshuai Wu, Arjan van der Schaft, Jian Chen

Abstract

In this paper, we study the robust trajectory tracking problem for a class of nonlinear systems with incremental passivity. The velocity of the desired trajectory and parts of the model information are unknown apart from boundedness assumptions. A velocity observer based method and a sliding mode controller are proposed while the asymptotic tracking result is guaranteed by a zero-state detectability condition for both cases. Unlike previous results, the studied systems are not necessarily feedback linearizable nor in a strict feedback form. The ball and beam system is utilized to illustrate the implementation of the proposed tracking control laws.

Keywords

Incremental passivity; Trajectory tracking; Robust control; Port-Hamiltonian systems; Asymptotic stability

Citation

BibTeX

@article{Wu_2019,
  title={{Robust trajectory tracking for incrementally passive nonlinear systems}},
  volume={107},
  ISSN={0005-1098},
  DOI={10.1016/j.automatica.2019.05.065},
  journal={Automatica},
  publisher={Elsevier BV},
  author={Wu, Chengshuai and van der Schaft, Arjan and Chen, Jian},
  year={2019},
  pages={595--599}
}

Download the bib file

References

  • Acary, V. & Brogliato, B. Implicit Euler numerical scheme and chattering-free implementation of sliding mode systems. Systems & Control Letters vol. 59 284–293 (2010) – 10.1016/j.sysconle.2010.03.002
  • Bartolini, G., Ferrara, A. & Usai, E. Chattering avoidance by second-order sliding mode control. IEEE Transactions on Automatic Control vol. 43 241–246 (1998) – 10.1109/9.661074
  • Brogliato, B., Ortega, R. & Lozano, R. Global tracking controllers for flexible-joint manipulators: a comparative study. Automatica vol. 31 941–956 (1995) – 10.1016/0005-1098(94)00172-f
  • Chen, J., Behal, A. & Dawson, D. M. Robust Feedback Control for a Class of Uncertain MIMO Nonlinear Systems. IEEE Transactions on Automatic Control vol. 53 591–596 (2008) – 10.1109/tac.2008.916658
  • Corless, M. & Leitmann, G. Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems. IEEE Transactions on Automatic Control vol. 26 1139–1144 (1981) – 10.1109/tac.1981.1102785
  • Demidovich, Dissipativity of a nonlinear system of differential equations. Vestnik Moscow State University, Ser. Mat. Mekh. Part I (1961)
  • Fischer, N., Kamalapurkar, R. & Dixon, W. E. LaSalle-Yoshizawa Corollaries for Nonsmooth Systems. IEEE Transactions on Automatic Control vol. 58 2333–2338 (2013) – 10.1109/tac.2013.2246900
  • Fridman, Higher order sliding modes as a natural phenomenon in control theory. (1996)
  • Galias, Z. & Yu, X. Euler’s Discretization of Single Input Sliding-Mode Control Systems. IEEE Transactions on Automatic Control vol. 52 1726–1730 (2007) – 10.1109/tac.2007.904289
  • Hauser, J., Sastry, S. & Kokotovic, P. Nonlinear control via approximate input-output linearization: the ball and beam example. IEEE Transactions on Automatic Control vol. 37 392–398 (1992) – 10.1109/9.119645
  • Hill, D. & Moylan, P. The stability of nonlinear dissipative systems. IEEE Transactions on Automatic Control vol. 21 708–711 (1976) – 10.1109/tac.1976.1101352
  • Hirschorn, R. M. Incremental sliding mode control of the ball and beam. IEEE Transactions on Automatic Control vol. 47 1696–1700 (2002) – 10.1109/tac.2002.803538
  • Isidori, (2013)
  • Khalil, (2002)
  • Lozano, R. & Brogliato, B. Adaptive control of robot manipulators with flexible joints. IEEE Transactions on Automatic Control vol. 37 174–181 (1992) – 10.1109/9.121619
  • Nakaoka, S., Nakazawa, A., Yokoi, K., Hirukawa, H. & Ikeuchi, K. Generating whole body motions for a biped humanoid robot from captured human dances. 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422) vol. 3 3905–3910 – 10.1109/robot.2003.1242196
  • Paden, B. & Sastry, S. A calculus for computing Filippov’s differential inclusion with application to the variable structure control of robot manipulators. IEEE Transactions on Circuits and Systems vol. 34 73–82 (1987) – 10.1109/tcs.1987.1086038
  • Pao, Transformation of human hand positions for robotic hand control. (1989)
  • Pavlov, A. & Marconi, L. Incremental passivity and output regulation. Systems & Control Letters vol. 57 400–409 (2008) – 10.1016/j.sysconle.2007.10.008
  • Reyes-Báez, (2016)
  • van der Schaft, (2017)
  • van der Schaft, A. & Jeltsema, D. Port-Hamiltonian Systems Theory: An Introductory Overview. Foundations and Trends® in Systems and Control vol. 1 173–378 (2014) – 10.1561/2600000002
  • Xian, B., Dawson, D. M., deQueiroz, M. S. & Chen, J. A Continuous Asymptotic Tracking Control Strategy for Uncertain Nonlinear Systems. IEEE Transactions on Automatic Control vol. 49 1206–1206 (2004) – 10.1109/tac.2004.831148
  • Xian, B., de Queiroz, M. S., Dawson, D. M. & McIntyre, M. L. A discontinuous output feedback controller and velocity observer for nonlinear mechanical systems. Automatica vol. 40 695–700 (2004) – 10.1016/j.automatica.2003.12.007
  • Yaghmaei, A. & Yazdanpanah, M. J. Trajectory tracking for a class of contractive port Hamiltonian systems. Automatica vol. 83 331–336 (2017) – 10.1016/j.automatica.2017.06.039