# Control of Implicit Dynamic Systems

# Scope

The goal of this project is the application of differential geometric methods for systems of nonlinear implicit differential equations, also known as differential algebraic equations (DAEs). The methods developed within this project cover algorithms to test implicit systems on properties related to control, as the observability, accessibility and the identifiability of a model parameter. These algorithms have been implemented in a computer algebra package for Maple.

# Description

With an approach based on transformation groups algorithms to test the properties accessibility and observability for implicit systems are derived, as well as the property identifiability of a system parameter. The idea of this concept is to relate the properties observability and identifiability to the nonexistence of certain transformation groups and the property accessibility to the existence of group invariants.

# Implementation

A computer algebra package for Maple has been developed which implements the mentioned algorithms. In order to increase the efficiency of the algorithms, methods of algebraic geometry are used, especially tools based on Buchbergers algorithm to calculate Groebner bases.

# More results

It can be shown that many operations, known within the differential geometric framework of modern control theory, can in principle be carried out directly at the implicit system as well.