Compensating for order variation in mesh refinement for direct transcription methods
When implicit Runge-Kutta methods are applied to stiff or differential algebraic equations, they may suffer a reduction of order. In the direct transcription approach to optimal control problems, the theory sometimes fails to accurately predict this reduction which may affect mesh refinement algorithms. The authors describe a new mesh refinement algorithm based on dynamically estimating the order reduction at different parts of the considered interval and on different iterations during the optimisation. The new method is demonstrated on a numerical example with fast transients at both ends of the considered interval.
scientific article; zbMATH DE number 1566009