Adaptive stabilization of a class of high‐order uncertain nonholonomic systems with unknown control coefficients

This paper is concerned with the globally stabilizing control design for a class of high‐order nonholonomic systems. Compared with the existing literature, the high‐order nonholonomic systems under investigations have more uncertainties and unknowns, such as neither lower nor upper bound is known for each control coefficient of the systems. This renders the existing control methods highly difficult to the control problems of the systems or even inapplicable. In this paper, by defining two new unknown parameters whose dynamic updating laws are properly chosen and also by using the discontinuous coordinates transformation and the method of adding a power integrator, a new design approach is given to the adaptive stabilizing controllers for the systems. A numerical simulation is provided to demonstrate the effectiveness of the theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.