Optimality-based grid adaptation for input-affine optimal control problems

This paper studies the solution accuracy of direct single-shooting in comparison to the solution of the continuous optimal control problem (OCP). First, a convergence relation between the solution of the nonlinear program and that of continuous OCP is analyzed by means of an exemplary problem. This example reveals that Pontryagin's minimum principle cannot be used as a stopping criterion for optimality-based control grid adaptation. Consequently, a novel grid refinement strategy is introduced, which is rather based on the switching function and thus limited to the class of input-affine OCPs. Grid points are eliminated and inserted such that the approximation of the optimality condition of the OCP, elucidated by the switching function, is improved. The suggested methodology is illustrated and compared to a previously published wavelet-based adaptation approach by means of two reactor optimization problems with different solution characteristics.