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Volume 43 Issue 1
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ZHU Weiqiu, YING Zuguang. ADVANCES IN RESEARCH ON NONLINEAR STOCHASTIC OPTIMAL CONTROL OF QUASI-HAMILTONIAN SYSTEMS[J]. Advances in Mechanics, 2013, 43(1): 39-55. doi: 10.6052/1000-0992-12-045
Citation: ZHU Weiqiu, YING Zuguang. ADVANCES IN RESEARCH ON NONLINEAR STOCHASTIC OPTIMAL CONTROL OF QUASI-HAMILTONIAN SYSTEMS[J]. Advances in Mechanics, 2013, 43(1): 39-55. doi: 10.6052/1000-0992-12-045
shu

ADVANCES IN RESEARCH ON NONLINEAR STOCHASTIC OPTIMAL CONTROL OF QUASI-HAMILTONIAN SYSTEMS

doi: 10.6052/1000-0992-12-045

  • Department of Mechanics, School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027, China

Funds:  The project was supported by the National Natural Science Foundation of China (10932009, 11072212, 11072215, 11272279).
More Information
  • Corresponding author: ZHU Weiqiu
  • Received Date: 2012-03-26
  • Rev Recd Date: 2012-11-14
  • Publish Date: 2013-01-24
    Abstract
  • Advances in the theory of nonlinear stochastic optimal control of quasi-Hamiltonian systems and its applications in the last decade is summarized. It includes: (1) the basic nonlinear stochastic optimal control strategies based on the stochastic averaging method for quasi-Hamiltonian systems and the stochastic dynamical programming principle, that is, response minimization control, stochastic stabilization, first-passage failure minimization control, and the control for targeting a specified stationary probability density function; (2) further study on the nonlinear stochastic optimal control for application, such as optimal control of partially observable systems, bounded optimal control, time-delay optimal control, semi-active optimal control and minimax control; (3) the integrated nonlinear stochastic optimal control strategy; (4) the applications of the nonlinear stochastic optimal control strategy to engineering structures including hysteretic systems and fractional derivative systems. Some related background and problems to be studied in future are also pointed out.

     

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