Conjugate points and shocks in nonlinear optimal control

Abstract

We investigate characteristics of the Hamilton-Jacobi-Bellman equation arising in nonlinear optimal control and their relationship with weak and strong local minima. This leads to an extension of the Jacobi conjugate points theory to the Bolza control problem. Necessary and sufficient optimality conditions for weak and strong local minima are stated in terms of the existence of a solution to a corresponding matrix Riccati differential equation.