Asymptotic series solution of singularly perturbed optimal control problems

✍ Scribed by P. Sannuti

• Publisher: Elsevier Science
• Year: 1974
• Tongue: English
• Weight: 873 KB
• Volume: 10
• Category: Article
• ISSN: 0005-1098
• DOI: 10.1016/0005-1098(74)90023-5

✦ Synopsis

Uniformly valid asymptotic approximations to a singularly perturbed nonlinear twopoint boundary value problem of optimal control theory may be constructed by a computationally simple method.

Snmmm'y--An optimal control problem of some nonlinear differential equations containing a small parameter is considered. This problem leads to a two-point boundary value problem (TPBVP) whose differential order can be reduced by neglecting the small parameter. In this paper an explicit method of constructing an asymptotic power series solution of the TPBVP as the small parameter tends to zero is presented. The method allows a separation of slow and fast dynamics in the problem while reducing the differential order of the equations. The determination of asymptotic series terms is computationally simple since one needs to solve only initial or final value problems instead of TPBVP's. The method has computational similarities with quasilinearization and second variation techniques.