Abstract
This paper proposes a new feedback control system based on a multirate sampled data control and a periodic switching for a class of nonholonomic systems in time-state control form. A coordinate transformation is introduced to transform the discretized nonholonomic system with a zero order hold and a sampler into a linear time-invariant discrete-time system. Moreover, a simple necessary and sufficient condition is derived to assure the controllability of the transformed linear system. The contributions are as follows. First, the problem of finding a controller to stabilize the nonholonomic systems is reduced to the well-known pole assignment problem. As a result, a simple and explicit design method of the stabilizing controllers is obtained. Secondly, a quadratic regulator problem is posed and is solved of finding a controller to minimize a cost functional consisting of the state and the control input. This minimization problem is reduced to a linear quadratic regulator (LQR) problem, and a simple design method of the optimal feedback gain is presented. Finally, a simulation for a two-wheeled vehicle demonstrates the effectiveness of the proposed method.
