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On the Characterization of Properly Relaxed Delayed Controls

โœ Scribed by J.F Rosenblueth; J Warga; Q.J Zhu

Book ID
102594349
Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
259 KB
Volume
209
Category
Article
ISSN
0022-247X

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โœฆ Synopsis

In previous papers Warga and Zhu have proven the conjecture of Rosenblueth and Vinter that a particular abstract model characterizes the set แ‘ฌ of relaxed ลฝ . controls that are limits of ordinary controls with possibly time-dependent delays. Rosenblueth and Vinter have also provided a simple and concrete characterization of แ‘ฌ for the case of constant delays that are consecutive multiples of a common divisor h. In the present paper we provide a concrete characterization of แ‘ฌ for the ลฝ . case of delays that are arbitrary and not necessarily consecutive multiples of some h. We also exhibit a simple compactification of the set of solutions of controlled differential equations with such delays in control.

๐Ÿ“œ SIMILAR VOLUMES

A Representation of Properly Relaxed Con
A Representation of Properly Relaxed Controls with Two Delays
โœ Javier F. Rosenblueth ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 186 KB

The search of a proper relaxation procedure in the sense that relaxed minimiz-. ers can be approximated with ordinary controls for optimal control problems involving delays in the control variables has been the main topic of several recent papers. Three models of relaxation, which we call the weak,

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A characterization of relaxed controls with commensurate delays
โœ J.F Rosenblueth ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 328 KB

The question of how to properly relax optimal control problems involving arbitrary commensurate delays in the controls was studied in a recent paper by characterizing, in terms of projections of a common probability measure, the weak star closure of the space of ordinary controls. In this paper, we