Computer algebra methods in control

This project deals with the nonlinear control systems defined on time scales and the aims of the project can be divided into two parts - improvement of mathematical theory and software development. The theoretical tasks are related with realization problem, i.e. recovering, if possible, the state equations form input-output description of the system. Our goals are the following: first, to construct the method for realization of the input-output equations on time scale in terms of non-commutative polynomials and second, to find the method for realization of the system given by its behavioural description, i.e. with its inputs and outputs not specified. Solution of the above problems is necessary for the software package, since it fills the gaps in existing theory. The second part of the project is devoted to the symbolic computer algebra software package for control systems on time scales, allowing to solve various modelling, analysis and synthesis problems. Most of the packages functions will be based on algebraic methods of differential one-forms and noncommutative polynomial rings. The programs will be written within computer algebra system Mathematica and they will be integrated with the existing nonlinear control package. The developed functions will be available on our nonlinear control website, so that everyone with the internet access can use them.