Solving Dynamic Optimization Problems to a Specified Accuracy: An Alternating Approach Using Integrated Residuals

We propose a novel direct transcription and solution method for solving nonlinear, continuous-time dynamic optimization problems. Instead of forcing the constraints to be satisfied only at selected number points as in collocation, new approach alternates between minimizing constraining squared norm constraint residuals integrated along whole trajectories. As result, can obtain solutions higher accuracy same mesh compared collocation methods, enables flexible tradeoff optimality, provides reliable challenging problems, including those with singular arcs high-index differential algebraic equations.