Computer algebra methods for feedback linearization using an exterior calculus framework

Abstract

The focus of this paper is on the use of exterior calculus approaches to the problem of static and dynamic state feedback linearization. The computer algebra program Maple/sup R/ is used to generate state and state feedback transformations using elements of the Lie symmetry package and custom code. For static feedback linearization, the GS algorithm has been implemented. For dynamic feedback linearization, necessary and sufficient conditions are introduced and implemented in the form of a generalized GS algorithm. The merits of the exterior calculus-based approach relative to existing vector field approaches are discussed, and several dynamic feedback linearizable systems are used to illustrate the implementation.