In recent years, a class of nonlinear stochastic optimal control strategies were developed by the present author and his co-workers for minimizing the response, stabilization and maximizing the reliability and mean first-passage time of quasi Hamiltonian systems based on the stochastic averaging method for quasi Hamiltonian systems and the stochastic dynamic programming principle. This review summaries the basic idea, procedures and applications of these strategies and pointes out necessary further work.

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