Numerical method for time-delay problems

✍ Scribed by Jerry L. Hanson

• Publisher: John Wiley and Sons
• Year: 1975
• Tongue: English
• Weight: 505 KB
• Volume: 9
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1620090108

✦ Synopsis

Abstract

Analytical solutions for linear systems with time‐delays are difficult, if not impossible, to obtain. This is particularly true in the synthesis of an optimal control for a system with time‐delays or of optimal strategies for a differential or difference game with delays. Some of these problems are discrete in nature while many others can be converted into a discrete format. Probably the most direct method of handling linear, discrete problems with time delays is by using an enlarged state vector to eliminate the delays. The main disadvantage of this technique is the increased dimensions of the resulting matrices. This paper shows, through an illustrative example, that these dimensions of the resulting matrices. This paper shows, through an illustrative example, that these dimensions (and thus the storage requirements and computational time) can be effectively reduced. Thus the method is computationally feasible for a larger class of problems than if standard matrix algebra routines were used.