Quasi-Invariant Optimal Control Problems

摘要: We study in optimal control the important relation between invariance of problem under a family transformations, and existence preserved quantities along Pontryagin extremals. Several extensions Noether theorem are provided, direction which enlarges scope its application. formulate more general version Noether's for problems, incorporates possibility to consider transformations depending on several parameters and, what is important, deal with quasi-invariant not necessarily invariant problems. trust that this latter extension provides new possibilities we illustrate it examples, covered by previous known versions theorem.