Stochastic optimal structural control: 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 as strong earthquakes, wind turbulences, and water waves. Thus, in case of dynamic disturbances, additional control elements can be installed enabling active control actions.Active control strategies for mechanical structures are applied in order to counteract heavy applied dynamic loads, such as earthquakes, wind, and water waves, which would lead to large vibrations causing possible damages of the structure. Modeling the structural dynamics by means of a system of first order random differential equations for the state vector (displacement vector q   and time derivative q˙ of q), robust optimal controls are determined in order to cope with the stochastic uncertainty in the applied loadings.

► Stochastic optimal controls are constructed by stochastic optimization methods. ► Stochastic optimal open-loop feedback controls yield robust optimal feedback laws. ► A stochastic version of the Hamilton–Jacobi theory is developed. ► Minimal controls and solutions of the related stochastic 2-point BVP are obtained. ► Optimal trajectories, controls and control laws are constructed in real-time.