Second-order conditions for optimal control problems with mixed state-control constraints

Presents second-order conditions for the optimal control problem with mixed state-control constraints. First, the conjugate point theory is developed and a necessary condition in terms of the corresponding Riccati equation is obtained. Sufficiency criteria are given in terms of strengthened necessary conditions including the Riccati equation. The author´s results are for the essentially bounded controls and hence, they generalize the known ones in the literature