Sliding mode control and chaos

In this chapter, we have examined the relationship between SMC and chaos. We have shown that digitising SMC in practice may cause some micro-level 'chaotic' behaviours, such as different periodic behaviours due to different initial conditions, an aspect of sensitivity to initial conditions. An interesting correlation between the periodic trajectories and their symbolic sequences has been explored. We have also discussed two SMC-based chaos control methods: one is the TDFC control and the other is a generalised OGY method. Their effectiveness has also been verified by computer simulations.