Construction of the Control Realizing the Rotation of a Timoshenko Beam

We consider the linear model of a slowly rotating Timoshenko beam in a horizontal plane whose moment is controlled by the angular acceleration of the disk of the driving motor into which the beam is clamped. This work complements our previous results on the controllability of the beam from a position of rest into another position of rest; we give a method of construction of a piecewise constant control solving the problem.     

Charakterisierung der eindeutigkeit bei der nichtlinearen gleichmäβigen approximation

Ohne Zusammenfassung Vorgelegt von L. Collatz     

Zur Dualitätstheorie bei linearen Optimierungsproblemen in halbgeordneten Vektorräumen

Ohne Zusammenfassung     

Zur verallgemeinerten rationalen Approximation

Ohne Zusammenfassung     

Lineare Optimierung in halbgeordneten Vektorräumen

Summary The problem of linear programming in partially ordered vector spaces is formulated as an immediate generalization of the same problem in Euclidean spaces. Sufficient conditions for the existence of solutions of the problem and its dual are obtained. In the special case of function spaces the sufficient conditions for the solvability of the dual problem are satisfied if a certain regularity condition is assumed.

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This research was supported by the Air Force Office of Scientific Research under grant AF-AFO SR-93 7-6 7     

Control and Game-Theoretical Treatment of a Cost-Security Model for Disarmament

In this paper a time-discrete dynamic model for the process of disarmament is investigated. The state variables of the system are costs and security values. We assume that the costs can be controlled, and we aim at reducing the costs to zero and achieving non-negative security values after a finite number of time steps. In the case where the opponents behave cooperatively this leads to the solution of a linear programming problem. If the opponents behave non-cooperatively, then a Nash equilibrium has to be determined under linear constraints. © 1997 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd. Math. Meth. Appl. Sci., Vol. 20, 653–666 (1997).     

On the controllability of a robot arm

Considered is the rotation of a robot arm or rod in a horizontal plane about an axis through the arm's fixed end and driven by a motor whose torque is controlled. The model was derived and investigated computationally by Sakawa and co-authors in [7] for the case that the arm is described as a homogeneous Euler beam. The resulting equation of motion is a partial differential equation of the type of a wave equation which is linear with respect to the state, if the control is fixed, and non-linear with respect to the control. Considered is the problem of steering the beam, within a given time interval, from the position of rest for the angle zero into the position of rest under a certain given angle. At first we show that, for every L²-control, there is exactly one (weak) solution of the initial boundary value problem which describes the vibrating system without the end condition. Then we show that the problem of controllability is equivalent to a non-linear moment problem. This, however, is not exactly solvable. Therefore, an iteration method is developed which leads to an approximate solution of sufficient accuracy in two steps. This method is numerically implemented and demonstrated by an example. © 1998 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd.     

On the approximate calculation of time-minimal distributed controls of vibrations by finite element approximations

This paper is concerned with distributed null-control of vibrations governed by an abstract wave equation. Based on a method for the exact computation of minimumL ²-norm controls for given time intervals and time-minimal controls which are bounded with respect to theL ²-norm, an approximation method is developed which is based on Galerkin's method ana convergence results are derived.This paper is based on U. Lamp's doctoral dissertation and was supported by the Deutsche Forschungsgemeinschaft.     

On signal processing with sampling errors: a worst case analysis

Summary In a communication system with sampling errors the worst case is considered where the minimal mean square error for a suitable choice of the transfer function becomes maximal. The transfer functions are allowed to be chosen from the space of all transfer functions of a given finite bandwidth which is a multiple of the Nyquist bandwidth. The problem of maximizing the minimal mean square error is shown to be equivalent to solving a certain linear approximation problem whose solution can be characterized in such a way as to allow for an explicit calculation of it in special cases.Dedicated to Professor H.-W. Knobloch on the occasion of his 60th birthdayThis research was supported by Deutsche Forschungsgemeinschaft.