Efficient and More Accurate Representation of Solution Trajectories in Numerical Optimal Control
For researchers in numerical optimal control, this method improves solution accuracy and efficiency, though it is an incremental improvement over existing residual minimization techniques.
The paper addresses inaccuracies in representing optimal control trajectories using interpolation schemes, proposing a method that minimizes integrated residual error to achieve higher accuracy with coarser meshes, reducing problem dimensions and computational cost.
We show via examples that, when solving optimal control problems, representing the optimal state and input trajectory directly using interpolation schemes may not be the best choice. Due to the lack of considerations for solution trajectories in-between collocation points, large errors may occur, posing risks if this solution is to be applied. A novel solution representation method is proposed, capable of yielding a solution of much higher accuracy for the same discretization mesh. This is achieved by minimizing the integral of the residual error for the overall trajectory, instead of forcing the errors to be zero only at collocation points. In this way, the requirement for mesh resolution can be significantly reduced, leaving the problem dimensions relatively small. This particular formulation also avoids some of the drawbacks found in the earlier work of integrated residual minimization, leading to more efficient computations.