An optimal nonlinear feedback control strategy for randomly excited structural systems

A strategy for optimal nonlinear feedback control of randomly excited struc tural systems is proposed based on the stochastic averaging method for quas i-Hamiltonian systems and the stochastic dynamic programming principle. A r andomly excited structural system is formulated as a quasi-Hamiltonian syst em and the control forces are divided into conservative and dissipative par ts. The conservative parts are designed to change the integrability and res onance of the associated Hamiltonian system and the energy distribution amo ng the controlled system. After the conservative parts are determined, the system response is reduced to a controlled diffusion process by using the s tochastic averaging method. The dissipative parts of control forces are the n obtained from solving the stochastic dynamic programming equation. Both t he responses of uncontrolled and controlled structural systems can be predi cted analytically. Numerical results for a controlled and stochastically ex cited Duffing oscillator and a two-degree-of-freedom system with linear spr ings and linear and nonlinear dampings, show that the proposed control stra tegy is very effective and efficient.