Abstract
This article contributes to a deeper understanding of Pontryagin’s maximum principle within the realm of optimal control problems that are subject to an infinite number of constraints on the state variable. We delve into the application of the Dubovitskii-Milyutin theory, which employs conical approximations around pivotal elements such as the objective function, the system of differential equations, and the constraints on both control and state variables. This theoretical framework provides a robust methodological approach to tackle the complexities introduced by infinite constraints. Furthermore, the inclusion of a detailed illustrative example not only elucidates the theoretical constructs but also underscores the practical applicability and relevance of this results. This example serves to bridge the gap between abstract theory and practical implementation, demonstrating how our findings can be employed to solve real-world problems characterized by an infinite constraint structure.
In honor to Dr. Zoltan Varga