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SIAM J. on Control and Optimization

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1966

Volume 4, Issue 4, pp. 577-744


Linear Optimal Control Problems

B. N. Pshenichniy

SIAM J. Control 4, pp. 577-593 (17 pages) | Cited 6 times

Online Publication Date: July 18, 2006

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On the Duality between Estimation and Control

J. D. Pearson

SIAM J. Control 4, pp. 594-600 (7 pages) | Cited 1 time

Online Publication Date: July 18, 2006

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The problem of smoothing is shown to be a variational dual to a problem of control or regulation. Two fundamental equations occur in both contexts which relate to an earlier duality principle.

Optimal Processes in Distributed Parameter Systems and Certain Problems in Invariance Theory

A. I. Egorov

SIAM J. Control 4, pp. 601-661 (61 pages) | Cited 8 times

Online Publication Date: July 18, 2006

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In this paper we investigate optimal processes in systems whose behavior is described by various boundary value problems for partial differential equations.

On the Optimality of a Totally Singular Vector Control: An Extension of the Green’s Theorem Approach to Higher Dimensions

George W. Haynes

SIAM J. Control 4, pp. 662-677 (16 pages) | Cited 5 times

Online Publication Date: July 18, 2006

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Exhaustive Equivalence Classes of Optimal Systems with Separable Controls

Ruey-Wen Liu and R. Jeffrey Leake

SIAM J. Control 4, pp. 678-685 (8 pages) | Cited 5 times

Online Publication Date: July 18, 2006

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For a given optimal feedback control problem two systems which have the same optimal feedback control laws and have identical Hamilton-Jacobi equations are said to be equivalent. A necessary and sufficient condition for the equivalence of two systems with separable controls is obtained; with this condition, one can generate exhaustive equivalence classes of optimal systems.

Some Remarks on Complete Controllability

H. O. Fattorini

SIAM J. Control 4, pp. 686-694 (9 pages) | Cited 29 times

Online Publication Date: July 18, 2006

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Addendum: On Exponential Stability of Linear Differential Systems

Nam P. Bhatia

SIAM J. Control 4, pp. 695-697 (3 pages)

Online Publication Date: July 18, 2006

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Bounded-Input Bounded-Output Stability of Nonlinear Time-Varying Differential Systems

P. P. Varaiya and R. Liu

SIAM J. Control 4, pp. 698-704 (7 pages) | Cited 6 times

Online Publication Date: July 18, 2006

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A Fixed-Point Method for a Minimum-Norm Control Problem

J. E. Rubio

SIAM J. Control 4, pp. 705-715 (11 pages) | Cited 1 time

Online Publication Date: July 18, 2006

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A method for obtaining the control which minimizes the terminal value of the norm of the state vector of a linear, time-varying system is presented. It is shown that the control that minimizes the linear functional given by the inner product $(\hat c,x(t_f))$, with $\hat c$ a fixed point of an operator $L_0$ and $x(t_f)$ the terminal state vector, also minimizes the norm of $x(t_f)$. The operator $L_0$ maps vectors $c$ of unity norm into vectors ${{x(t_f )} / {\| {x(t_f )} \|}}$, with $x(t_f)$ obtained by applying the control that minimizes $(c,x(t_f))$.

Necessary Conditions for Singular Extremals Involving Multiple Control Variables

B. S. Goh

SIAM J. Control 4, pp. 716-731 (16 pages) | Cited 27 times

Online Publication Date: July 18, 2006

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New necessary conditions are obtained from the second variation, via a transformed accessory minimum problem, for an important class of singular Bolza problems, which includes most of the singular optimal control problems that have been studied in recent years. This set of necessary conditions is a generalization of the classical Clebsch (Legendre) necessary condition. It is in a form easily used. For problems with multiple control variables, it is required that a certain matrix be symmetric; and if this symmetry property is satisfied, it then requires another matrix to be positive semidefinite. The positive semidefiniteness of the diagonal terms of the latter matrix imposes the same conditions as those obtained by other authors (Kelley, Kopp and Moyer). Should this generalized Clebsch condition be satisfied only in a semidefinite manner, then another similar set of necessary conditions can deduced, and so on.
Three examples are studied. Firstly, we impose new necessary conditions on the variable thrust arcs of a rocket moving in a resisting medium in a vertical plane of a flat earth with two degrees of freedom, namely, the lift and thrust programs. Secondly, the doubly singular arcs of a problem in interplanetary guidance, formulated by Breakwell, are shown to be nonoptimal. Thirdly, a simple optimality condition is deduced for a class of identically singular optimal control problems, certain members of which were previously studied by Haynes, using an extension of the Green’s Theorem approach to higher dimension.

On Stationary Points of Nonlinear Maximum-Problems in Banach Spaces

K. Kirchgässner and K. Ritter

SIAM J. Control 4, pp. 732-739 (8 pages)

Online Publication Date: July 18, 2006

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An Example Concerning Rockets Capable of Impulsive Thrust

R. W. Rishel

SIAM J. Control 4, pp. 740-744 (5 pages)

Online Publication Date: July 18, 2006

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Abstract Unavailable
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