Exact controllability of a micro beam with boundary bending moment

ABSTRACT

In this paper, we show the exact controllability of a micro beam with boundary bending moment at time T > 0, which gives a confirmative answer to the open problem proposed by P. Guzmán and J. Zhu. The semi-group approach is adopted in investigation. The asymptotic spectral expression of the micro beam system is presented to verify an observability inequality for the dual system. By the duality principle, the exact controllability of the system is then established.

KEYWORDS:

• Micro beam
• boundary control
• exact controllability
• spectral analysis

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

National Natural Science Foundation of China [grant number 61673061].