After winning the second prize of National Natural Science Award in 2002, the research team led by Prof. ZHU Weiqiu, put forward and developed a stochastic average method for non-gaussian white noise excitation and non-classical (including delay, delay and fractional derivative damping, etc.) multidegree strongly nonlinear system with multiple degrees of freedom on the basis of the developed stochastic excitation dissipated Hamiltonian system theory. It is used for the response, stability and reliability study of the system. In order to solve the problem of optimal control of multiple different targets and multiple non-ideal factors in a multi-dof nonlinear stochastic system under multiple random excitation, the team proposed and developed non-linear stochastic optimal control design methods aiming at minimum response, maximum stability margin, maximum reliability, maximum average life and given stable probability density respectively. At the same time, an optimal control method is developed to solve the partial observable and uncertain, the time-delay of the actual control force, the boundedness and the incomplete implementation of the optimal control law.
