Output feedback asymptotic stabilization of nonholonomic systems with uncertainties

This paper is concerned with the asymptotic stabilization problem for a class of nonholonomic systems with uncertainties. The uncertain nonlinearities involved in the systems are assumed to be bounded by continuous functions of the outputs multiplied by measured states and unmeasured states. Our design outline is as follows. First, by using the input-state scaling technique, the nonholonomic systems can be converted into triangular nonlinear systems. Second, a dynamic gain observer is provided for the converted triangular nonlinear systems. Third, by choosing the appropriate state transformation, the problem of designing controller can be converted into the problem of constructing a dynamic system with r as its state. Last, a dynamic system with r as its state is constructed by estimating the nonlinearities, and stability analysis of the closed-loop control system is conducted by using the Lyapunov stability theory. Contrary to many existing control designs for nonholonomic systems, the celebrated backstepping design is not utilized here.