A minimax stochastic optimal semi-active control strategy for stochastically excited quasi-integrable Hamiltonian systems with parametric uncertainty by using magneto-rheological (MR) dampers is proposed. Firstly, the control problem is formulated as an n-degree-of-freedom (DOF) controlled, uncertain quasi-integrable Hamiltonian system and the control forces produced by MR dampers are split into the passive part and the semi-active part. Then the passive part is incorporated into the uncontrolled system. After that, the stochastic optimal semi-active control problem is solved by applying the minimax stochastic optimal control strategy based on the stochastic averaging method and stochastic differential game. The worst-case disturbances and the optimal controls are obtained by the minimax dynamical programming equation with the constraints of disturbance bounds and MR damper dynamics. Finally, the system response and the control performance are evaluated by using Monte Carlo simulation. An example of a two-DOF system with coupling damping and parametric uncertainty under Gaussian white noise excitations is worked out in detail to illustrate the procedure and effectiveness of the proposed control strategy, which is also compared with the clipped linear-quadratic-Gaussian control strategy to show the advantages.
Feng, J., Ying, Z-G., Zhu, W-Q., & Wang, Y. (2012). A minimax stochastic optimal semi-active control strategy for uncertain quasi-integrable Hamiltonian systems using magneto-rheological dampers. Journal of Vibration and Control, 18(13), 1986-1995. https://doi.org/10.1177/1077546311429058