A dynamic compensator for in-domain control of Burgers' equation

Abstract

This paper addresses the problem of output regulation control of a Burgers' equation under pointwise in-domain actuation. A dynamic compensator that generates the in-domain control is developed for output regulation of the considered system. A nonlinear boundary feedback control is used to ensure the closed-loop stability of the Burgers' equation. The proposed control scheme is implemented by means of Adomian decomposition method and flatness-based trajectory planning. A numerical simulation study is carried out, and the obtained results demonstrate the efficiency and effectivity of the proposed approach.

Keywords:

• Burgers' equation
• nonlinear feedback control
• dynamic compensator
• Adomian decomposition method
• differential flatness

Acknowledgements

The authors thank the anonymous reviewers for their constructive comments, which helped to improve the quality and presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Guchuan Zhu http://orcid.org/0000-0003-2117-6796

Additional information

Funding

This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) under Grant RGPIN-2018-04571.