Necessary optimality conditions for a class of control problems with state constraint
In this work, the authors study necessary conditions of optimal control problems with pathwse state constraints involving ordinary differential equations. The motivation to study such a problem arises out of the fact that existing classifications of necessary conditions using gradient-based approaches are quite abstract and are difficult to verify. The authors use the idea of the needle variations in Pontryagin's maximum principle classification of optimality condition, to develop verifiability conditions that distinguish the controls to which the needle technique of optimality verification can be effectively applied. The authors also provide a geometric interpretations of such conditions. Finally, they demonstrate the validity of their theoretical results with several numerical examples. The paper is well-written and easy to follow, and is certainly quite a good contribution to the field of optimal control. It will be interesting for researchers working on optimal control to use and validate the theoretical results of this paper in different applications. Moreoever, it will also be interesting to see if such an idea can be extended to optimal control problems involving partial differential equations.
scientific article; zbMATH DE number 7434008