Numerical solution of optimal control problems with constant control delays

We investigate a class of optimal control problems that exhibit constant exogenously given delays in the control in the equation of motion of the differential states. Therefore, we formulate an exemplary optimal control problem with one stock and one control variable and review some analytic properties of an optimal solution. However, analytical considerations are quite limited in case of delayed optimal control problems. In order to overcome these limits, we reformulate the problem and apply direct numerical methods to calculate approximate solutions that give a better understanding of this class of optimization problems. In particular, we present two possibilities to reformulate the delayed optimal control problem into an instantaneous optimal control problem and show how these can be solved numerically with a stateof- the-art direct method by applying Bock’s direct multiple shooting algorithm. We further demonstrate the strength of our approach by two economic examples.

Design and Test of a 0.5 THz Dipole Antenna With Integrated Schottky Diode Detector on a High Dielectric Constant Ceramic Electromagnetic Bandgap Substrate

This paper presents the first analysis of the input impedance and radiation properties of a dipole antenna, placed on top of Fan 's three-dimensional electromagnetic bandgap (EBG) structure, (Applied Physics Letters, 1994) constructed using a high dielectric constant ceramic. The best position of the dipole on the EBG surface is determined following impedance and radiation pattern analyses. Based on this optimum configuration an integrated Schottky heterodyne detector was designed, manufactured and tested from 0.48 to 0.52 THz. The main antenna features were not degraded by the high dielectric constant substrate due to the use of the EBG approach. Measured radiation patterns are in good agreement with the predicted ones.

Das Judentum im 19. und 20. Jahrhundert : Vortrag, geh. in Hamburg am 29. Dez. 1909

von Max Nordau

Das Judentum im 19. und 20. Jahrhundert : Vortrag, gehalten in Hamburg am 29. Dez. 1909

von Max Nordau

Das altjüdische Erziehungs- und Unterrichtswesen im Lichte moderner Bestrebungen : Vortrag gehalten in der 368. Vollversammlung der "Wiener Pädagogischen Gesellschaft" am 3. April 1909

S. Frankfurter

Geschichte der israelitischen Kranken-Verpflegungs-Anstalt und Beerdigungs-Gesellschaft zu Breslau : zur Einweihungs-Feier d. Fränckelschen Hospitals am 1. Sept. 1841

von J. Grätzer