Optimal nonlinear stochastic control of hysteretic systems

W. Q. Zhu, Z. G. Ying, Yiqing Ni, J. M. Ko

Research output: Journal article publicationJournal articleAcademic researchpeer-review

72 Citations (Scopus)


A strategy for optimal nonlinear stochastic control of hysteretic systems with parametrically and/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 1D 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.
Original languageEnglish
Pages (from-to)1027-1032
Number of pages6
JournalJournal of Engineering Mechanics
Issue number10
Publication statusPublished - 1 Jan 2000

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering


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