Computational Aspects of Homogeneous Approximations of Nonlinear Systems

The objective of the paper is to describe computational methods and techniques of investigation of certain algebraic structures needed in order to apply the results in concrete problems in mathematical control theory of nonlinear systems. Contemporary theoretic research requires more and more sophisticated tools for a possible application of the results. In the paper we propose computational tools and techniques for a certain type of simplification of driftless control systems. Such simplification still preserve most crucial properties of the original ones like controllability, but the simplified system have a special feedforward form that is much easier to integrate or allows to solve other problems in control theory. We present the computational procedure and foundations of the library as the extension of existing software libraries in Python language. The approach is illustrated with some numerical experiments and simulations. We conclude with a discussion about related computational issues.