Guidance and stable and unstable manifolds with input

✍ Scribed by Louis R. Hunt; George Meyer; Viswanath Ramakrishna

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 123 KB
• Volume: 9
• Category: Article
• ISSN: 1049-8923
• DOI: 10.1002/(sici)1099-1239(199902)9:2<85::aid-rnc394>3.0.co;2-r

✦ Synopsis

The theory in this paper is motivated by the problem of aircraft guidance in automatic flight control, in which plant models are nonlinear. This leads us to consider the stable inversion problem, which in turn can be cast as the problem of finding a bounded solution of a time-varying nonlinear system subject to a bounded input. Under the appropriate assumptions there is a unique bounded (for all time) continuous solution to this time-varying nonlinear system in response to the bounded (for all time) input. We show that there is a (local) stable manifold containing all bounded continuous solutions for non-negative time, and that all such solutions converge to the aforementioned unique solution as time goes to infinity. Likewise there is a (local) unstable manifold containing all bounded solutions for non-positive time and these converge to the unique solution as time goes to minus infinity. In fact, the unique solution (cross the time axis) is the intersection of the stable and unstable manifolds.