2019 Chinese Control Conference (CCC) | 2019
On Near-controllability of Discrete-time Bilinear Systems from A Geometric Point of View
Abstract
Near-controllability is a recently established concept which can be used to not only better characterize nonlinear systems but also prove their controllability. In this paper, we consider near-controllability of a class of discrete-time bilinear systems. For the systems with system matrix having only real eigenvalues, the near-controllability problem has been solved. However, for the case when the system matrix has complex eigenvalues, the near-controllability problem is unsolved and the challenges remain. In order to deal with the near-controllability problem in the complex eigenvalues case, we propose a geometric method. It is shown that the proposed geometric method works for (near-)controllability of the two-dimensional systems and an algorithm is constructed to derive control sequences based on this method. Moreover, this method may be developed to attack high-dimensional case of the near-controllability problem.