Necessary Conditions for Optimal Control Problems: Conjugate Points
Vera M. Zeidan, P. Zezza · SIAM Journal on Control and Optimization · 1988
In this paper we introduce a definition of “normality” and of “conjugate points” for a general optimal control problem. Using these concepts we obtain new second-order necessary conditions for optimality. In the special case when the control set U is the whole space or in the classical setting of calculus of variations, our conditions reduce to known results, namely, the Jacobi condition and the existence of a solution to a certain Riccati equation.