Optimal Structural Control under Stochastic Uncertainty: Stochastic Optimal Open-Loop Feedback Control

In order to stabilize mechanical structures under dynamic applied loads, active control strategies are taken into account. The structures usually are stationary, safe and stable without external dynamic disturbances, such a strong earthquakes, wind turbulences, water waves, etc.. Thus, in case of dynamic disturbances, additional control elements can be installed enabling active control actions. Active control (or regulation) strategies for mechanical structures are applied in order to counteract heavy applied dynamic loads, which would lead to large vibrations causing possible damages of the structure. Modeling the structural dynamics by means of a system of first order linear random differential equations for the state vector (displacement vector q and time derivative of q), stochastic optimal feedback controls are required in order to take into account the stochastic uncertainties in the applied loadings. Based on the stochastic Hamiltonian of the control problem, stochastic optimal feedback laws are constructed by means of the open- loop feedback control method in combination with finite dimensional stochastic optimization methods.