Application of the Return Method to the Steering of Nonlinear Systems
The controllability property plays a crucial role in mathematical control theory. For linear systems, necessary and sufficient conditions of controllability are given by the Kalman criterion. This criterion also allows to study the local controllability by linear approximation . There is a number of necessary as well as sufficient conditions of controllability for nonlinear systems expressed in terms of properties of the corresponding Lie algebra (see, e.g., [2, 7, 9]). However, in general case, a constructive test of controllability of nonlinear systems is a difficult problem and, to our knowledge, there is no effective estimate of the number of iterated Lie brackets for the test of an appropriate rank condition . In this paper, we use controllability conditions of nonlinear systems based on a modification of the return method (cf. [4, 6, 8]).
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