Contribution to the programme of “Unified geometric theory of control (UGTC)”

The rapid developments in modern technology require complex distributed parameter regulators. In spite of about 40 years development and progress in the theory of distributed parameter systems (DPS) we do not have a powerful enough theory or even adequate language for formulation and solving of problems. The UGTC-programme was born to try to overcome these disadvantages. This programme is a consequence of natural developments in the geometric theory of phase portraits for differential inclusions. The geometrical trend in control is quite coherent with the common trends in the modern sciences, in particular, in mechanics and theoretical physics. The key notion of UGTC is the notion of structure defined in a sufficiently wide and exact mathematical sense of this term. All other main concepts of control theory are made in terms of structures. Hence the UGTC can be also considered as a unified structural approach to the different kinds of control problems. In UGTC the investigation of phenomenon is considered as an investigation of respective structures or symmetries standing behind phenomenon on the subject of their formal determination, conservation (invariance), destruction (violation), transformation, or control. Here from this stand point we briefly consider a class of differential systems