Gaussian Mixture Penalty for Trajectory Optimization Problems

We consider the task of solving an aircraft trajectory optimization problem where the system dynamics have been estimated from recorded data. Additionally, we want to avoid optimized trajectories that go too far away from the domain occupied by the data, since the model validity is not guaranteed outside this region. This motivates the need for a proximity indicator between a given trajectory and a set of reference trajectories. In this presentation, we propose such an indicator based on a parametric estimator of the training set density. We then introduce it as a penalty term in the optimal control problem. Our approach is illustrated with an aircraft minimal consumption problem and recorded data from real flights. We observe in our numerical results the expected trade-off between the consumption and the penalty term.