Local Controllability in the Problem with Variable Structure

With this paper we investigate the controllability with changing phase space problem. There has recently been a growing interest in controllability problems of variable structure because of the expansion of their practical application area. Such problems arise in physics, biology, and economics. On the given time intervals, our problem of transferring an object from the given set of space to the given set of other space through a point zero is considered. The motion of an object is expressed via two nonlinear systems of differential equations, and the controlling influence of the system has a specific form due to physical applications. The transition of the object from initial space to second is specified by some mapping. Concerning the problem at which the nonlinear system in the first space - it is locally zero-controlled, plus the righthand part of the system in the other space admits linearization under some conditions, sufficient controllability conditions are obtained.