Nonlinear stochastic optimal control of partially observable linear structures

A strategy for nonlinear stochastic optimal control of partially observable linear structures is proposed and illustrated with linear building structures equipped with control devices and sensors under horizontal ground acceleration excitation. The control problem of a partially observable structure is first converted into that of a completely observable structure based on the separation principle. Then, a partially averaged control system of Itô equations is obtained from the completely observable structure by using the stochastic averaging method for quasi-Hamiltonian systems. Dynamical programming equations for finite and infinite time-interval controls are established based on the stochastic dynamical programming principle and solved to obtain the optimal control law and value function. Finally, the response of controlled structure is obtained from solving the Fokker–Planck–Kolmogorov equation associated with the fully averaged system of Itô equations. The numerical results for a five-story building structure model are obtained by using the proposed control strategy and compared with those by using linear quadratic Gaussian control strategy to show the effectiveness and efficiency of the proposed strategy.