Multi-input control-affine systems static feedback equivalent to a triangular form and their flatness

ABSTRACT

In this paper, we give a complete geometric characterisation of systems locally static feedback equivalent to a triangular form compatible with the chained form, for m = 1, respectively with the m-chained form, for m ≥ 2, where the number of controls is m + 1. They are x-flat systems. We provide a system of first-order PDE's to be solved in order to find all x-flat outputs, for m = 1, respectively all minimal x-flat outputs, for m ≥ 2. We illustrate our results by examples, in particular, by an application to a mechanical system: the coin rolling without slipping on a moving table.

KEYWORDS:

• Flatness
• triangular form
• chained form
• flat outputs
• static feedback equivalence
• control-affine systems

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by Natural Science Foundation of China [grant number 61573192]; the Natural Science Foundation of the Jiangsu Higher Education Institutions [grant number 14KJB120004]; and the Talents National III Program of the Institute of Cyber-Systems and Control, Zhejiang University [grant number B07031].