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 …

In this paper we give a complete description of how the Jacobi theory of conjugate points
can be extended to a regular linear-quadratic control problem where the state end-points …

In this work, we derive second order necessary and sufficient optimality conditions for a
discrete optimal control problem with one variable endpoint and the other fixed, and with …

For an optimal control problem we define a second variation which is invariant under
change of coordinates, and realize it as a linear-quadratic problem. When the strong …

The principal aim of this paper is to state and prove the so-called Reid roundabout theorem
for the symplectic dynamic system (S) z Δ=\cal S tz on an arbitrary time scale\Bbb T, so that …

In this work we derive the accessory problem for a general nonlinear discrete optimal control
problem. We obtain necessary conditions for optimality—nonnegativity of the second …

Admissible directions and generalized coupled points for optimal control problems | Nonlinear
Analysis: Theory, Methods & Applications skip to main content ACM Digital Library home ACM …

The purpose of this paper is to give the Reid``Roundabout Theorem''for quadratic
functionals with general boundary conditions. In particular, we describe the so-called …

In this paper, we give the definitions of conjugate and semi-conjugate points for a quadratic
elliptic form in a Hilbert space, and we state the corresponding necessary and sufficient …

This paper presents extended sufficiency results for the local minimality of an extremal of the
Bolza problem. These results provide an essential improvement in the state of the art …