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SIAM J. on Control and Optimization

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1963

Volume 1, Issue 3, pp. 241-376


A Sufficient Condition in the Theory of Optimal Control

E. B. Lee

J. Soc. Indus. and Appl. Math. Ser. A 1, pp. 241-245 (5 pages) | Cited 7 times

Online Publication Date: July 18, 2006

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Abstract Unavailable

Generalized Curves and the Existence of Optimal Controls

R. A. Gambill

J. Soc. Indus. and Appl. Math. Ser. A 1, pp. 246-260 (15 pages)

Online Publication Date: July 18, 2006

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Abstract Unavailable

On the Existence of Optimal Feedback Controls

T. F. Bridgland, Jr.

J. Soc. Indus. and Appl. Math. Ser. A 1, pp. 261-274 (14 pages) | Cited 2 times

Online Publication Date: July 18, 2006

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Abstract Unavailable

Relay Type Control Systems with Retardation and Switching Delay

M. N. Oğuztőrelí

J. Soc. Indus. and Appl. Math. Ser. A 1, pp. 275-289 (15 pages)

Online Publication Date: July 18, 2006

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In the present paper, we wish to investigate relay type control systems with retardation and switching delay. For this purpose, we extend some basic results on the continuation of solutions which are due to J. Andre and P. Seibert. Also, we extend some stability theorems of R. Bellman and K. L. Cooke, making use of their kernel function representation of the solutions. We also consider the dependence of the solutions upon switching delay.

A Time Optimal Control Problem for Systems Described by Differential Difference Equations

M. N. Oǧuztöreli

J. Soc. Indus. and Appl. Math. Ser. A 1, pp. 290-310 (21 pages) | Cited 3 times

Online Publication Date: July 18, 2006

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The aim of this paper is to establish the solution of an optimal time control problem for a physical system whose state is described by a linear differential-difference equation with retarded argument. We have obtained here a generalisation of the results of Bellman and his collaborators Glicksberg, Gross and Kalaba, and of LaSalie and Neustadt by using a technique due to LaSalle, with the help of the kernel matrix representation of Bellman and Cooke and also a new integral representation for the solutions of linear differential-difference equations.

Stability Criteria for Nonlinear Ordinary Differential Equations

O. L. Mangasarian

J. Soc. Indus. and Appl. Math. Ser. A 1, pp. 311-318 (8 pages) | Cited 2 times

Online Publication Date: July 18, 2006

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The main results of this work are three sufficient conditions for the (1) stability, (2) uniform asymptotic stability in the large and (3) instability, of the equilibrium point $x = 0$ of the system of differential equations: $\dot x = f(t,x)$, $f(t,0) = 0$. Stated roughly these conditions are: The point $x = 0$ is (1) stable if $x'f(t,x)$ is a concave function of $x$, (2) uniformly asymptotically stable in the large if $x'f(t,x)$ is a concave function of $x$ is a strictly concave function of $x$, and (3) unstable if $x'f(t,x)$ is a strictly convex function of $x$. These results are obtained by using the stability and instability criteria of Liapunov and properties of concave and convex functions.

On Computing Optimal Control with Inequality Constraints

Yu-Chi Ho and Piero B. Brentani

J. Soc. Indus. and Appl. Math. Ser. A 1, pp. 319-348 (30 pages)

Online Publication Date: July 18, 2006

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Abstract Unavailable

A Solution of the Goddard Problem

Boris Garfinkel

J. Soc. Indus. and Appl. Math. Ser. A 1, pp. 349-368 (20 pages)

Online Publication Date: July 18, 2006

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The problem of optimizing the thrust of a vertically ascending rocket is solved here under the assumption of isothermal atmosphere in two important cases: 1) the jet Mach number and the fuel supply are sufficiently large; 2) the drag is a convex function of the velocity.
The first case embraces all physical drags and is valid for the Earth; the second extends to all atmospheres, but is restricted to drags that arc fairly common.
With impulsive boosts in velocity admitted, the solution is shown to contain a finite number of such boosts in the sonic region of the rocket velocity, and to contain no coasting arcs except in the terminal stage.
An absolute minimum is proved with the aid of a sufficient condition applicable to problems of optimum control.

A Remark on “A New Partial Differential Equation for the Stability Analysis of Time Invariant Control Systems”

G. P. Szegö and G. R. Geiss

J. Soc. Indus. and Appl. Math. Ser. A 1, pp. 369-376 (8 pages)

Online Publication Date: July 18, 2006

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Abstract Unavailable
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