Nonlinear stochastic optimal control of tall buildings under wind loading

A nonlinear stochastic optimal (NSO) control strategy for wind-excited tall buildings is proposed. The power spectral density (PSD) matrix of the fluctuating part of wind velocity vector is diagonalized in eigenvector space. Each element of the diagonalized PSD matrix is modeled as a set of second-order linear filters driven by white noise. A stochastic optimal control problem of partially observable system is formulated and converted into a stochastic optimal control problem of completely observable system based on the separation principle. The latter problem is solved by using the NSC strategy based on the stochastic averaging method for quasi-Hamiltonian systems and the dynamic programming principle. The response statistics of both uncontrolled and controlled structures is predicted analytically. A numerical example is given to show better control effectiveness and efficiency of the proposed NSO controller than those of linear quadratic Gaussian (LQG) controller.