S. M. Khryashchev
Russia, 195251, Saint-Petersburg, Politechnicheskaya st., 29,
S.-Petersburg State Technical University,
Dept. of Higher Mathematics,
G. S. Osipenko
Russia, 195251, Saint-Petersburg, Politechnicheskaya st., 29,
S.-Petersburg State Technical University,
Dept. of Higher Mathematics,
A new constructive method based on symbolic dynamics methods is proposed for the study of the global controllability of a dynamical system. Methods of applied symbolic dynamics were effectively used for a qualitative analysis of the global behavior of dynamical systems without control. The base of applied symbolic dynamics methods is available in papers by G.S.Osipenko. The study of the controllability is realized by replacing a dynamical control system with its symbolic image that is a directed graph. This graph can be viewed as a finite discrete approximation of a dynamical system. The symbolic image keeps many features of the initial dynamical control system. The method does not require any preliminary information on a system and uses only certain assumptions of the general character. In particular, the local controllability along trajectories is required. This property is known to be generic and can be easily verified. All necessary estimates can be made by using methods of numerical and symbolic calculations. The main result states that a dynamical control system is controlled if and only if its symbolic image is controlled. The controllability of the symbolic image can be tested by a computer.