2018/05/29 by Bruno Hérissé, Hérissé, Bruno, Riccardo Bonalli +3
Mathematics · #FOS: Mathematics #Optimization and Control (math.OC) #math.OC
paper · pdf · doi:10.48550/arxiv.1805.11990
arXiv admin note: text overlap with arXiv:1709.04383
arxiv created 2018/11/12 · arxiv updated 2018/11/13
Consider a general nonlinear optimal control problem in finite dimension, with constant state and/or control delays. By the Pontryagin Maximum Principle, any optimal trajectory is the projection of a Pontryagin extremal. We establish that, under appropriate assumptions, Pontryagin extremals depend continuously on the parameter delays, for adequate topologies. The proof of the continuity of the trajectory and of the control is quite easy, however, for the adjoint vector, the proof requires a much finer analysis. The continuity property of the adjoint with respect to the parameter delay opens a new perspective for the numerical implementation of indirect methods, such as the shooting method. We also discuss the sharpness of our assumptions.