A FAS approach for stabilization of generalized chained forms: part 2. Continuous control laws

In this paper, continuous time-varying stabilizing controllers for the type of general nonholonomic systems proposed and treated in part 1 are designed using the fully actuated system (FAS) approach. The key step is to differentiate the first scalar equation, and by control of the obtained second-order scalar system, a proportional plus integral feedback form for the first control variable is obtained. With the solution to this designed second-order scalar system, the rest equations in the nonholonomic system form an independent time-varying subsystem which is then handled by the FAS approach. The overall designed controller contains an almost arbitrarily chosen design parameter, and is proven to guarantee the uniformly and globally exponential stability of the closed-loop system. The proposed approach is simple and effective, and is demonstrated with a practical example of ship control.