Analysis of controlled morse type Frenkel-Kontorova model

The Frenkel-Kontorova (FK) model describes a one-dimensional particle array of N identical particles moving on a surface. This model attracts much attention due to its broaden application in many fields. A control problem for this model proposed in many papers is how to render the average velocity of the whole system reach a commanded value. In this study, an output feedback control law is designed to solve the proposed control problem. The main contribution of this paper is that the dynamics of single particles for FK model with morse type interaction under the designed control law is investigated using Lyapunov method. Computer simulation shows the interesting properties of single particles investigated.