Optimal nonlinear feedback control strategy for randomly excited structural systems

A strategy for optimal nonlinear feedback control of randomly excited structural systems is proposed based on the stochastic averaging method for quasi-Hamiltonian systems and the stochastic dynamic programming principle. A randomly excited structural system is formulated as a quasi-Hamiltonian system and the control forces are divided into conservative and dissipative parts. The conservative parts are designed to change the integrability and resonance of the associated Hamiltonian system and the energy distribution among the controlled system. After the conservative parts are determined, the system response is reduced to a controlled diffusion process by using the stochastic averaging method. The dissipative parts of control forces are then obtained from solving the stochastic dynamic programming equation. Both the responses of uncontrolled and controlled structural systems can be predicted analytically. Numerical results for a controlled and stochastically excited Duffing oscillator and a two-degree-of-freedom system with linear springs and linear and nonlinear dampings, show that the proposed control strategy is very effective and efficient.