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Low-complexity robust tracking of high-order nonlinear systems with application to underactuated mechanical dynamics

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Abstract

This paper presents a low-complexity design approach with predefined transient and steady-state tracking performance for global practical tracking of uncertain high-order nonlinear systems. It is assumed that all nonlinearities and their bounding functions are unknown and the reference signal is time varying. A simple output tracking scheme consisting of nonlinearly transformed errors and positive design parameters is presented in the presence of virtual and actual control variables with high powers where the error transformation technique using time-varying performance functions is employed. Contrary to the existing results using known nonlinear bounding functions of model nonlinearities, the proposed tracking scheme can be implemented without using nonlinear bounding functions (i.e., the feedback domination design), any adaptive and function approximation techniques for estimating unknown nonlinearities. It is shown that the tracking performance of the proposed control system is ensured within preassigned bounds, regardless of high-power virtual and actual control variables. The motion tracking problem of an underactuated unstable mechanical system with unknown model parameters and nonlinearities is considered as a practical application, and simulation results are provided to show the effectiveness of the proposed theoretical result.

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Acknowledgements

This research was supported by the Human Resources Development (No. 20174030201810) of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government Ministry of Trade, Industry and Energy, by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2016R1D1A1B03931312), and by the Ministry of Science and ICT (MSIT), Korea, under the Information Technology Research Center (ITRC) support Program (IITP-2017-2014-0-00636) supervised by the Institute for Information and communications Technology Promotion (IITP).

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  1. School of Electrical and Electronics Engineering, Chung-Ang University, 84 Heukseok-Ro, Dongjak-Gu, Seoul, 156-756, Republic of Korea

    Sung Jin Yoo

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Yoo, S.J. Low-complexity robust tracking of high-order nonlinear systems with application to underactuated mechanical dynamics. Nonlinear Dyn 91, 1627–1637 (2018). https://doi.org/10.1007/s11071-017-3969-0

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