This paper is devoted to the study of necessary or sufficient second-order conditions for a weak local minimum in an optimal control problem. The problem is stated in the Mayer form and includes equality constraints both on the endpoints and on the state-control trajectory. The second-order conditions are stated through an associated linear-quadratic problem.
Optimality conditions for a constrained control problem / G. Stefani; P. Zezza. - In: SIAM JOURNAL ON CONTROL AND OPTIMIZATION. - ISSN 0363-0129. - STAMPA. - 34:(1996), pp. 635-659. [10.1137/S0363012994260945]