Hamiltonian dynamical systems for convex problems of optimal control: implications for the value function

For fully convex problems of optimal control, the Hamiltonian dynamical system provides a global description of evolution of the subdifferentials of the value function from those of the initial cost. We employ this description and the convex structure of the problem to investigate the differentiability properties of the value function. Motivation is provided by questions of regularity of optimal feedback, the key ingredients of which the the value function, and by the fact that the Hamiltonian may lead to a reasonable dynamical system, even if the underlying control problem involves various constraints and penalties.