Analysis of sufficient optimality conditions with a set of Lyapunov type functions

For the classical optimal control problem with general endpoints constraints new variants of the Krotov–Carathéodory type global optimality conditions and sufficient conditions of the so-called Hamilton–Jacobi canonical optimality theory are proposed and compared. These sufficient optimality conditions are obtained and formulated by using some support set of nonsmooth Lyapunov-type functions, which are strongly monotone with respect to the control dynamic system. It is proved that the sufficient optimality conditions corresponding to the canonical theory are more efficient. Some properties of Lyapunov functions from the support set are investigated.