Several problems in structural control of modern civil engineering structures are summarized. Then, the stochastic averaging for quasi-Hamilton system, stochastic dynamics programming principle and the nonlinear stochastic optimal control strategy for quasi-Hamilton system are introduced. The nonlinear stochastic optimal control strategy for quasi-integrable Hamilton systems is used to study the vibration control of offshore platform structures under wave loading, of tall building structures under wind loading with partially observable information and of tall building structures under wind loading by using semi-active control with MR/ER dampers. Comparison with LQG control strategy shows that the nonlinear stochastic optimal control strategy for quasi-Hamilton systems is better than LQG control strategy in terms of control effectiveness and control efficiency. For the proposed semi-active stochastic optimal control strategy using MR/ER dampers, if certain conditions are satisfied, MR/ER dampers can fully produce the required optimal control forces without clipping, and its performance is superior to that of clipped LQG semi-active control strategy.
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