Hamilton‐Jacobi inequalities and the optimality conditions in the problems of control with common end constraints

The canonical theory of the necessary and sufficient conditions for global optimality based on the sets of nonsmooth solutions of the differential Hamilton‐Jacobi inequalities of two classes of weakly and strongly monotone Lyapunov type functions was developed. These functions enable one to estimate from above and below the objective functional of the optimal control problem and determine the internal and external approximations of the reachability set of the controlled dynamic system.