Differential flatness of two one-forms in arbitrary number of variables

✍ Scribed by M. Rathinam; R.M. Murray

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 133 KB
• Volume: 36
• Category: Article
• ISSN: 0167-6911
• DOI: 10.1016/s0167-6911(98)00104-2

✦ Synopsis

Given a di erentially at system of ODEs, at outputs that depend only on original variables but not on their derivatives are called zero-at outputs and systems possessing such outputs are called zero-at. In this paper we present a theory of zero-atness for a system of two one-forms in arbitrary number of variables (t; x 1 ; : : : ; x N ). Our approach splits the task of ÿnding zero-at outputs into two parts. First part involves solving for distributions that satisfy a set of algebraic conditions. The second part involves ÿnding an integrable distribution from the solution set of the ÿrst part. Typically this part involves solving PDEs. Our results are also applicable in determining if a control a ne system in n states and n -2 controls has at outputs that depend only on states. We illustrate our method by examples.