Hamilton-Jacobi equations for nonlinear descriptor systems

Optimal control problems for nonlinear descriptor systems are considered. An approach where the descriptor system is conceptually reduced to a state space form is compared to an approach where the Hamilton-Jacobi equation is directly formulated for the descriptor system. The two approaches are shown to give essentially the same systems of equations to be solved. A certain unknown function is present only in the second approach but is shown to be computable from the quantities common to both approaches