van Nieuwstadt, Michiel and Rathinam, Muruhan and Murray, Richard M. (1995) Differential Flatness and Absolute Equivalence. California Institute of Technology . (Unpublished) http://resolver.caltech.edu/CaltechCDSTR:1995.CIT-CDS-94-006
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In this paper we give a formulation of differential flatness---a concept originally introduced by Fleiss, Levine, Martin, and Rouchon---in terms of absolute equivalence between exterior differential systems. Systems which are differentially flat have several useful properties which can be exploited to generate effective control strategies for nonlinear systems. The original definition of flatness was given in the context of differentiable algebra, and required that all mappings be meromorphic functions. Our formulation of flatness does not require any algebraic structure and allows one to use tools from exterior differential systems to help characterize differentially flat systems. In particular, we shown that in the case of single input control systems (i.e., codimension 2 Pfaffian systems), a system is differentially flat if and only if it is feedback linearizable via static state feedback. However, in higher codimensions feedback linearizability and flatness are *not* equivalent: one must be careful with the role of time as well the use of prolongations which may not be realizable as dynamic feedbacks in a control setting. Applications of differential flatness to nonlinear control systems and open questions will be discussed. Revised 14 Aug 95
|Item Type:||Report or Paper (Technical Report)|
|Group:||Control and Dynamical Systems Technical Reports|
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|Deposited On:||23 Sep 2002|
|Last Modified:||18 Mar 2015 23:23|
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