Tracking control of a class of non-linear systems with applications to cruise control of air-breathing hypersonic vehicles

Abstract

A new tracking-control method for general non-linear systems is proposed. A virtual controller and some command references are introduced to asymptotically stabilise the system of the tracking error dynamics. Then, the actual controller and command references are derived by solving a system of linear algebraic equations. Compared with other tracking-control methods in the literature, the tracking-controller design in this paper is simple because it needs only to solve a system of linear algebraic equations. The boundedness of the tracking controller and command references is guaranteed by the solvability of the terminal value problem (TVP) of an ordinary differential equation. For non-linear systems with minimum-phase properties, the TVP is automatically solvable. A numerical example shows that the tracking-control method is still available for some systems with non-minimum-phase properties. To enhance the robustness of the tracking controller, a non-linear disturbance observer (NDO) is introduced to estimate the disturbance. The combination of the tracking controller and the NDO is applied to the tracking control of an air-breathing hypersonic vehicle.

Keywords:

• non-linear systems
• asymptotic tracking
• terminal value problem
• non-minimum-phase
• air-breathing hypersonic vehicle

Acknowledgements

The authors would like to thank Michael McAllister for proofreading the paper.

Additional information

Funding

This work is supported by National Natural Science Foundation of China [grant number 61273153], [grant number 61374037].