Abstract:
A brief review of the works on the modified theory of invariant variational problems and its applications, developed by the author, is presented. The research is based on the infinitesimal Li–Ovsyannikov formalism and E. Noether's fundamental idea of invariant functionals. Theorems on generalized invariance are proved, and the application of the developed theory to the solution of optimal problems of mathematical physics is discussed.
Keywords:Lee group, integral invariant, functional invariance, Noether's generalized theorem, Pontryagin's maximum principle, Bellman's equation.
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