Non-linear stochastic optimal control for coupled-structures system of multi-degree-of-freedom

Coupled structures under random excitation are modelled as a quasi-integrable Hamiltonian system of multi-degree-of-freedom and the reduced-order model in structural mode space is formulated. A non-linear stochastic optimal control method for the system is presented. The non-linear optimal control of adjacent tall building structures coupled with supplemental control devices and under random seismic excitation is performed by using the proposed method. First, applying the stochastic averaging method to the system yields Itô stochastic differential equations for modal vibration energy processes, so that the system energy control is conducted generally instead of the system state control and the dimension of the control problem is reduced. Then applying the stochastic dynamical programming principle to the controlled diffusion processes yields a dynamical programming equation, taking into account random excitation spectra. An explicit polynomial solution to the equation is proposed to determine the non-linear optimal control forces. Furthermore, the response statistics of the controlled non-linear coupled structures under random seismic excitation are evaluated by using the stochastic averaging method, and are compared with those of the uncontrolled structures to determine the control efficacy. Numerical results illustrate the high control effectiveness and efficiency of the proposed non-linear stochastic optimal control method for coupled structures as a quasi-integrable Hamiltonian system.