Index criteria for differential algebraic equations arising from linear-quadratic optimal control problems

The index of DAE systems arising from linear quadratic optimal control problems is considered. Necessary and sufficient conditions ensuring regularity with tractability index one are proved. Then, it is shown that if the control problem DAE is regular with index one and if the leading term of the DAE to be controlled is given by one full-column-rank and one full-row-rank matrix, then it has a Hamiltonian inherent explicit ODE. For problems with regular index zero or index one DAEs to be controlled, the DAE of the control problem is shown to be regular with tractability index one or three, depending on whether the control coefficient R is singular.