Computer Algebra algorithms for the test on accessibility and observability for implicit dynamical systems

This contribution is devoted to computer algebra based algorithms for the analysis of systems of implicit ordinary differential equations. These systems are identified with submani-folds in a suitable jet space. It is outlined how the accessibility and observability test for implicit ordinary differential equations can be solved via an approach utilizing transformation groups, which has been already published. Since this approach requires systems in formally integrable form, an algorithm for the derivation of this form is presented and it is shown, how Groebner bases can be successfully applied in the case of implicit systems with polynomial nonlinearities. In addition, the algorithms for the tests on observability and accessibility according to the proposed approach are sketched.