OPTIMAL NONLINEAR STOCHASTIC CONTROL OF HYSTERETIC SYSTEMS

Many civil engineering structures exhibit hysteresis when subjected to severe dynamic loading. Structural systems incorporated with passive base isolation devices or electromagneto-rheological dampers also exhibit hysteretic behavior. Furthermore, engineering structures often undergo random loading such as wind and earthquake. Therefore, random vibration of hysteretic systems is a significant subject in nonlinear stochastic structural dynamics. A strategy for optimal nonlinear stochastic control of hysteretic systems with parametrically or externally random excitations is proposed and illustrated with an example of a single-degree-of-freedom system. A hysteretic system subject to random excitation is first replaced by a nonlinear nonhysteretic stochastic system, from which an Ito equation for the averaged total energy of the system as a one-dimensional controlled diffusion process is derived by using the stochastic averaging method of energy envelope. For a given performance index, a Hamilton-Jacobi-Bellman equation is then established based on the stochastic dynamical programming principle and solved to yield the optimal control force. Finally, the statistics of the responses of uncontrolled and controlled systems and those of the optimal control force are predicted analytically. Comparison with the modified optimal polynomial controller indicates that the proposed strategy is more effective and efficient.

  • Availability:
  • Supplemental Notes:
    • This study was partially supported for the first two writers by the National Natural Science Foundation of China (under Grant No. 19672054) and by Cao Guang Biao Hi-Science-Technology Foundation of Zhejiang University and Hong Kong Polytechnic University.
  • Corporate Authors:

    American Society of Civil Engineers

    1801 Alexander Bell Drive
    Reston, VA  United States  20191-4400
  • Authors:
    • Zhu, W Q
    • Ying, Z G
    • Ni, Y Q
    • Ko, J M
  • Publication Date: 2000-10

Language

  • English

Media Info

Subject/Index Terms

Filing Info

  • Accession Number: 00800616
  • Record Type: Publication
  • Contract Numbers: 19672054, DE-FG03-95ER14500
  • Files: TRIS
  • Created Date: Oct 13 2000 12:00AM