Stochastic Optimal Control of Structures Based on Explicit Time-Domain Method

Stochastic optimal control of structures involves the optimal design of the control law and the optimal selection of the weighting parameters adopted in the control law. The classical stochastic optimal control (CSOC) method for linear quadratic Gaussian (LQG) control problems needs to employ the assumption of Gaussian white noise excitation, and the numerical solution to the Riccati equation in deriving the control law leads to the difficulty in obtaining closed-form sensitivities with respect to the weighting parameters, which further makes it difficult to use the gradient-based optimization algorithms for the optimal selection of those parameters. In this study, an explicit stochastic optimal control (ESOC) method is developed based on the explicit time-domain method (ETDM). With the explicit formulation of structural responses, the constraint of the optimal control problem imposed by the equation of motion of the structure can be satisfied automatically, which avoids the introduction of the Riccati equation with the Gaussian white noise assumption, and therefore the optimal control can be implemented under general random excitations. On this basis, the closed-form sensitivities of the response statistics with respect to the weighting parameters are obtained for the controlled structure, which are further incorporated into the gradient-based method of moving asymptotes (MMA) for the stochastic optimal selection of the weighting parameters. Numerical examples are worked out to demonstrate the efficacy of the proposed method for the stochastic optimal control of structures.