Lagrangian submanifold landscapes of necessary conditions for maxima in optimal control: Global parameterizations and generalized solutions.

We construct global generating functions of the initial and of the evolution Lagrangian submanifolds related to a Hamiltonian flow. These global parameterizations are realized by means of Amann—Conley—Zehnder reduction. In some cases, we have to to face generating functions that are weakly quadratic at infinity; more precisely, degeneracy points can occurs. Therefore, we develop a theory which allows us to treat possibly degenerate cases in order to define a Chaperon—Sikorav—Viterbo weak solution of a time-dependent Hamilton-Jacobi equation with a Cauchy condition given at time t = T ( T > 0). The starting motivation is to study some aspects of Mayer problems in optimal control theory. [ABSTRACT FROM AUTHOR]