Global smooth time-varying exponential stabilization of nonholonomic chained form systems

It is well known that nonholonomic chained form systems cannot be stabilized by continuous pure state feedback. The solutions include time-varying feedback stabilization and discontinuous time-invariant feedback stabilization. Most of the existing time-varying control results suffer from the drawback that the designed control laws are very complex. Moreover, the control laws using smooth time-varying feedback do not stabilize the system with exponential convergence rate. It is pointed out that controlling nonholonomic chained form systems with discontinuous controls may be difficult to implement. In this paper smooth time-varying feedback control laws, which globally stabilize the system with exponential convergence rate, are developed. Besides the advantage of design simplicity, the convergence rate of each state can be specified in a prior. The method has no constraints on the initial value of states. The simulation results show the efficiency of this method.