Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (5): 1465-1491.

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Stability and Optimality of 2-D Mindlin-Timoshenko Plate System

Chunguo Zhang*(),Yuzhi Fu,Yubiao Liu   

  1. Department of Mathematics, College of Science, Hangzhou Dianzi University, Hangzhou 310018
  • Received:2020-02-21 Online:2021-10-26 Published:2021-10-08
  • Contact: Chunguo Zhang
  • Supported by:
    the NSFC(61374096)


In this paper, 2-D Mindlin Timoshenko plate system with local boundary control is studied. By using the receding horizon control method, the infinite time domain optimality problem is transformed into the finite time domain optimality problem. With the help of the multiplier technique, a priori estimation is made for any finite time domain system, and the observability inequality is obtained, which proves that the energy of the system is uniformly exponentially decay. Furthermore, with the aid of dual system, by means of the variational principle and Bellman optimality principle, the suboptimal conditions of the system in infinite time domain are obtained, and it is proved that the optimal trajectory is also exponential decay.

Key words: 2-D Mindlin Timoshenko plate, Receding horizon control method, Optimality, Exponential decay

CLC Number: 

  • O231.4