CONSTRAINED REGULAR LQ-CONTROL PROBLEMS

In this paper we give a complete description of how the Jacobi theory of conjugate points can be extended to a regular linear-quadratic cont rol problem where the state end-points are jointly constrained to belo ng to a subspace of R-n x R-n and there is a linear pointwise state-co ntrol constraint, We introduce also the definition of semiconjugate po int which describes a distinctive feature of these problems and state the corresponding necessary and sufficient conditions for the quadrati c form to be nonnegative or coercive. In the case in which the constra ints and the costs act separately on the initial and final points we g ive equivalent characterizations of the coercivity of the quadratic fo rm by means of the solutions of an associated Riccati equation in both the controllable and uncontrollable case.