Order of spatial discretization error in the discretized distributed parameter state regulator problem

✍ Scribed by J.M. Davis; W.R. Perkins

• Publisher: Elsevier Science
• Year: 1971
• Tongue: English
• Weight: 796 KB
• Volume: 292
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(71)90101-3

✦ Synopsis

The study considers the order of the error in the approximation to the optimal system response, control and performance cost of the distributed parameter linear state regulator problem. This error is incurred through uning a fcnite difference approximation to effect spatial discretization of the distributed parameter system and the subsequent application of the optimization algorithms for ordinary differential equations. The results are stated in a theorem from which several conclusions are drawn.

The usual conclusion is obtained that at a fixed time as the spatial increment site tends to zero the approximate system response, control and performance cost tends to the true optimal system response, control and cost. Two new conclusions are aLo drawn. They are that for a fixed spatial increment size the approximate system response may be close to the true system response only for times close to the initial time and the approximate control may be close to the true optimal control only for times close to the final time. An example illustrates the conclsions.