The Time-Optimal Control Problem of a Kind of Petrowsky System

• Main Authors: Dongsheng Luo, Wei Wei, Hongyong Deng, Yumei Liao
• Format: Article
• Language: English
• Published: MDPI AG 2019-03-01
• Series: Mathematics
• Subjects: Petrowsky system; time-optimal control; null-controllability; existence of time-optimal control; bang-bang property
• Online Access: https://www.mdpi.com/2227-7390/7/4/311

In this paper, we consider the time-optimal control problem about a kind of Petrowsky system and its bang-bang property. To solve this problem, we first construct another control problem, whose null controllability is equivalent to the controllability of the time-optimal control problem of the Petrowsky system, and give the necessary condition for the null controllability. Then we show the existence of time-optimal control of the Petrowsky system through minimum sequences, for the null controllability of the constructed control problem is equivalent to the controllability of the time-optimal control of the Petrowsky system. At last, with the null controllability, we obtain the bang-bang property of the time-optimal control of the Petrowsky system by contradiction, moreover, we know the time-optimal control acts on one subset of the boundary of the vibration system.