Optimal nonlinear feedback with feedforward control of high speed aerospace vehicles using a spatial statistical approach

The control of dynamical systems in the presence of uncertainty and disturbances must include state feedback for acceptable performance. However, the real-time optimal control of aerospace vehicles is challenging because of the computational time required to generate an ab initio optimal trajectory at every time step starting from the current state. Thus practical control systems assume that the actual trajectory lies in the neighborhood of the nominal optimal trajectory, and generate control perturbations using feedback gains determined using the nominal trajectory. Alternative methods implement optimal feedback controllers using control interpolation over a pre-computed extremal field, i.e. a family of open-loop optimal trajectories. Nevertheless, optimal feedback (FB) controllers can show reduced performance and accuracy in systems subject to significant disturbances. If such disturbances can be measured in real-time, this information can be fed forward to the controller for higher performance due to a more complete knowledge of the system environment. This work presents a methodology for the implementation of optimal nonlinear feedback+feedforward (FB+FF) controllers using kriging regression on extremal fields. This work also shows the implementation of FB+FF controllers on multiphase systems, i.e. trajectories with different dynamics on distinct phases. The proposed method is illustrated in the real-time optimal control of a high speed aerospace vehicle in the presence of realistic wind conditions.