ZG tracking control of Lu system with multiple inputs and with division-by-zero problem solved

This paper aims at solving the tracking-control problem of the Lu chaotic system with multiple inputs. As we know, the input-output linearization method may not solve the tracking-control problem of the Lu chaotic system because of the existence of division-by-zero problem, where the Lu chaotic system fails to have a well-defined relative degree. By combining Zhang dynamics (ZD) and gradient dynamics (GD), a new effective controller-design method, termed Zhang-gradient (ZG) method, is proposed in this paper for tracking control of the Lu chaotic system with multiple inputs (i.e., two and three inputs). This ZG method, with division-by-zero problem solved, is capable of solving the tracking-control problems of the Lu chaotic systems. Simulation verifications further demonstrate that the tracking controllers based on the ZG method can not only achieve satisfactory tracking accuracy but also successfully solve the division-by-zero problem encountered in the tracking-control process.