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Online optimisation-based backstepping control design with application to quadrotor

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posted on 24.06.2016, 10:08 authored by Hao Lu, Cunjia LiuCunjia Liu, Matthew CoombesMatthew Coombes, Lei Guo, Wen-Hua ChenWen-Hua Chen
In backstepping implementation, the derivatives of virtual control signals are required at each step. This study provides a novel way to solve this problem by combining online optimisation with backstepping design in an outer and inner loop manner. The properties of differential flatness and the B-spline polynomial function are exploited to transform the optimal control problem into a computationally efficient form. The optimisation process generates not only the optimised states but also their finite order derivatives which can be used to analytically calculate the derivatives of virtual control signal required in backstepping design. In addition, the online optimisation repeatedly performed in a receding horizon fashion can also realise local motion planning for obstacle avoidance. The stability of the receding horizon control scheme is analysed via Lyapunov method which is guaranteed by adding a parametrised terminal condition in the online optimisation. Numerical simulations and flight experiments of a quadrotor unmanned air vehicle are given to demonstrate the effectiveness of the proposed composite control method.


This work was supported by National Basic Research Program of China (2012CB720003), National Natural Science Foundation of China (61127007, 61121003, and 61320106010). Hao Lu would like to thank the Chinese Scholarship Council for supporting his study in the United Kingdom.



  • Aeronautical, Automotive, Chemical and Materials Engineering


  • Aeronautical and Automotive Engineering

Published in

IET Control Theory & Applications


LU, H. ... et al., 2017. Online optimisation-based backstepping control design with application to quadrotor. IET Control Theory and Applications, 10(14), pp. 1601–1611.


© Institution of Engineering and Technology


AM (Accepted Manuscript)

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This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

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This paper is a preprint of a paper accepted by IET Control Theory and Applications and is subject to Institution of Engineering and Technology Copyright. The final version is available : http://dx.doi.org/10.1049/iet-cta.2015.0976.