Computer Algebra Algorithms for the Differential Geometric Design of AI - Systems

For a special class of nonlinear systems, the so called AI - systems, some effective tools based on differential geometry for the solution of the analysis and synthesis problems are available. The differential geometric approach allows on the one hand a coordinate free formulation of dynamical systems and on the other hand the extension of well known concepts of linear systems to the nonlinear case. These methods require a great amount of symbolic operations, why the use of computer algebra programs is absolutely necessary. In this contribution we discuss several algorithms for the investigation of the accessibility, observability, input state and input output exact linearization of AI - systems. Finally two nontrivial application examples will demonstrate the efficiency of the proposed pocedures.