Stochastic dynamics and fractional optimal control of quasi integrable Hamiltonian systems with fractional derivative damping

In the present survey, some progress in the stochastic dynamics and fractional optimal control of quasi integrable Hamiltonian systems with fractional derivative damping is reviewed. First, the stochastic averaging method for quasi integrable Hamiltonian systems with fractional derivative damping under various random excitations is briefly introduced. Then, the stochastic stability, stochastic bifurcation, first passage time and reliability, and stochastic fractional optimal control of the systems studied by using the stochastic averaging method are summarized. The focus is placed on the effects of fractional derivative order on the dynamics and control of the systems. Finally, some possible extensions are pointed out.