A piecewise smooth switching control algorithm for chained systems

In this paper, a simple control approach is proposed for the multi-chain systems. This method is based on a switching algorithm of two sets of smooth steering laws. Global exponential convergence of all states is guaranteed. More importantly, the convergence rate is given explicitly. Two concrete methods are proposed for the design of steering laws. One is based on the backstepping design, another is based on the use of Riccati equation. Extension of this approach to some driftless systems is also discussed. This approach is very flexible in the sense that the requirement on the generator is very weak. Therefore, there is a great freedom in the determination of the generator which may be used to satisfy other control specifications.