Limit Cycle Generation for Multi-Modal and 2-Dimensional Piecewise Affine Control Systems

Abstract

This paper considers a limit cycle control problem of a multi-modal and 2-dimensional piecewise affine control system. Limit cycle control means a controller design method to generate a limit cycle for given piecewise affine control systems. First, we deal with a limit cycle synthesis problem and derive a new solution of the problem. In addition, theoretical analysis on the rotational direction and the period of a limit cycle is shown. Next, the limit cycle control problem for piecewise affine control system is formulated. Then, we obtain matching conditions such that the piecewise affine control system with the state feedback law corresponds to the reference system which generates a desired limit cycle. Finally, in order to indicate the effectiveness of the new method, a numerical simulation is illustrated. paper. The outline of this paper is as follows. We first consider a limit cycle synthesis problem and derive its new solution in Section II. Some theoretical properties are also shown. Then, in Section III, a formulation of limit cycle control problem is presented, and necessary and sufficient conditions for the problem, which are called matching conditions, are derived. Finally, a numerical simulation is shown in order to confirm the effectiveness of the new method in Section IV.