In 1959 AF Filippov published a paper [l] containing a lemma designed for use in the study
of optimal control problems. Stated somewhat imprecisely, let k be a continuous function on …

I. Introduction. Ascoli's theorem deals with continuous functions and states that the space of
bounded, equicontinuous functions is compact. The present paper extends it to the …

2. Results. Throughout this note denotes a positive Radon measure [2, p. 41 ft.] defined ona
compact Hausdorff space T, and (X, pl),(Y, denote metric spaces. We assume withoutloss of …

1. Introduction. Let us begin by recalling a theorem which insur an optimal control exists for a
rather general class of deterministic p Using vector notation, let X=(Xx,••• Xn), U=(f/i,••• Uk) …

1. Introduction. An undergraduate student of mathematics, or science, or engineering, is
usually introduced to an assortment of integrals. First he meets the onedimensional Darboux …

Before I begin this talk, I would like to sketch briefly what I plan to do. I hope to speak of
some of the important stages of the development of the calculus of variations, with a …

1. Introduction. The development of the mathematical theory of optimal control began in the
early to mid 1950's, partially in response to problems in various branches of engineering …

A Proof of Lusin's Theorem Page 1 1981] MATHEMATICAL NOTES 191 Solutions to
these problems as well as to problems in previous Olympiads may be obtained from Professor …

As usual we denote by I [x, u] f0 (t, x, u) dt the" cost," that is, the functional which has to be
minimized, by uu (t), t< __<= t, the" con-trol function" with values u (t)(u,..., u,) in a given …

In the present paper we give existence theorems for weak and usual solutions of (one-
dimensional problems) of calculus of variations and optimal control written in the Mayer …