Generalized Hamilton-Jacobi-Bellman equations in optimal control problems with phase constraints. I (Q1320783)

The authors consider a generalized form of the Hamilton-Jacobi-Bellman equation for optimal control problems with phase constraints. For problems where the optimal value function is nonsmooth this equation is replaced by two inequalities. Difficulties arise when phase constraints are present leading to cases where these inequalities do not hold. An example is given. In this paper conditions are given under which the first inequality is valid. A companion paper (following review) supplies conditions for the second inequality to hold.