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 paper, we present a survey and refinement of our recent results in the discrete optimal
control theory. For a general nonlinear discrete optimal control problem (P), second order …

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 …

Discrete quadratic functionals with variable endpoints for variable stepsize symplectic
difference systems are considered. A comprehensive study is presented for characterizing …

In this paper we provide a survey of characterizations of the nonnegativity and positivity of
discrete quadratic functionals which arise as the second variation for nonlinear discrete …

In this paper we study the relation between the coercivity and positivity of a time scale
quadratic functional J, which could be a second variation for a nonlinear time scale calculus …

The present article will appear 30 years after Hermann's report [840] was published; in that
report, the foundations of a new direction in optimal control theory, later called geometrical …

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 work we study nonnegativity and positivity of a discrete quadratic functional with
separately varying endpoints. We introduce a notion of an interval coupled with 0, and …

Archives of Inequalities and Applications 1 (2003) 1-7 DIAGONALIZATION APPROACH TO
DISCRETE QUADRATIC FUNCTIONALS 1. INTRODUCTIO Page 1 Archives of Inequalities and …