How to verify optimal controls computed by direct shooting methods? – A tutorial

摘要: Abstract For the solution of optimal control problems, direct methods have been established in process engineering community. If set up correctly they robustly provide more or less accurate approximations exact solution. In usual practice, neither distance to is reflected, nor compliance with continuous necessary conditions form Pontryagin's Minimum Principle checked. At end, some approximate available but its quality at question. This tutorial addresses problem verification controls computed by shooting methods. We focus on this popular transcription method though results are also relevant for other strategies. review known spread mathematical literature show how output nonlinear programs (NLPs) resulting from single transcriptions problems can be interpreted context Principle. particular, we adjoint variables means dual information provided NLP solver. Based approximation use a multi-level setting construct an estimate true extremal satisfying optimality. A comprehensive case study illustrates theoretical results.