Nonlinear stochastic optimal control of viscoelastic systems

A nonlinear stochastic optimal control strategy for single degree-of-freedom viscoelastic systems with strongly nonlinear stiffness under Gaussian white noise excitation is proposed. First, the viscoelastic system is converted into an equivalent nonlinear non-viscoelastic system by replacing the viscoelastic force with amplitude-dependent stiffness and damping. Second, the partially averaged Ito stochastic differential equation for total system energy as one-dimensional controlled diffusion process is derived by using the stochastic averaging method of energy envelope. For the semi-infinite time-interval ergodic control, the dynamical programming equation is established based on the dynamical programming principle and is solved to yield the optimal control force. Finally, the variances of the responses of controlled and uncontrolled systems and that of the optimal control force are predicted analytically. Numerical results show that the proposed control strategy is very effective and efficient.