STOCHASTIC OPTIMAL CONTROL FOR THE RESPONSE OF QUASI NON-INTEGRABLE HAMILTONIAN SYSTEMS

<正> A strategy is proposed based on the stochastic averaging method for quasi non-integrable Hamiltonian systems and the stochastic dynamical programming principle.The pro-posed strategy can be used to design nonlinear stochastic optimal control to minimize the responseof quasi non-integrable Hamiltonian systems subject to Gaussian white noise excitation.By usingthe stochastic averaging method for quasi non-integrable Hamiltonian systems the equations ofmotion of a controlled quasi non-integrable Hamiltonian system is reduced to a one-dimensional av-eraged It stochastic differential equation.By using the stochastic dynamical programming princi-ple the dynamical programming equation for minimizing the response of the system is formulated.The optimal control law is derived from the dynamical programming equation and the boundedcontrol constraints.The response of optimally controlled systems is predicted through solving theFPK equation associated with It stochastic differential equation.An example is worked out indetail to illustrate the application of the control strategy proposed.