Mixed Bernstein-Fourier Approximants for Optimal Trajectory Generation with Periodic Behavior
This research introduces a mixed Bernstein-Fourier approximation method for generating optimal trajectories in autonomous systems. It decomposes functions into nonperiodic (Bernstein) and periodic (Fourier) parts to create a robust, computationally efficient model. The method provides rigorous error bounds and guarantees that the approximated solutions converge to the true optimal trajectory as the approximation order increases.