Vol. 35, No. 2, 1970

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Focal points in a control problem

Edward Yoshio Mikami

Vol. 35 (1970), No. 2, 473–485

This paper applies a few results on quadratic forms in Hilbert space and the theory of focal points from a paper by Hestenes to a linear control problem with a constraint equation. The abnormality inherent in this problem allows focal intervals to exist. The main results are, after assuming the strengthened Clebsch condition, the following: (1) The signature is equal to the sum of the focal points on the open interval, (2) The focal points are the discontinuous points of rank and abnormality of the conjugate base matrix, and (3) The dimension of a maximal linear space of broken transversal extremal arcs is less than or equal to n a, where a is the abnormality of the problem.

Mathematical Subject Classification
Primary: 49.20
Received: 19 November 1969
Published: 1 November 1970
Edward Yoshio Mikami