Optimal Time-delay Control Of Ouasi Integrable Hamiltonian Systems Under Combined Harmonic And Wide-Band Random Excitations

The optimal time-delay control of quasi intergrable Hamiltonian systems under combined harmonic and wide-band random excitations is studied. First, the optimal control problem of quasi-integrable Hamiltonian systems under combined harmonic and wide-band random excitations is formulated. Then, the optimal time-delay control forces are approximately expressed in terms of the system state variables without time delay, and the system is converted into an traditional quasi-integrable Hamiltonian system without time-delay terms. Considering the possible resonant relations between natural frequencies and harmonic excitations frequencies, the system state is represented by energy and phase difference. A set of new partly averaged Ito equations are obtained by using the generalized harmonic functions averaging method. And the Hamilton-Jacobi-Bellman (HJB) equations are derived by using the stochastic dynamical programming principle. Finally, the optimal control forces can be obtained and the responses of such systems investigated can be predicted by solving the Fokker-Planck-Kolmogorov (FPK) equation associated with the fully averaged Ito equations or by using Monte Carlo simulation. As an example, the optimal time-delay control of the longitudinal vibration of a submarine propeller system is worked out in detail to illustrate the effectiveness and efficiency of the proposed control strategy.