Adaptive NN stabilization of uncertain nonholonomic mechanical systems

In this paper, an adaptive neural network (NN) controller is proposed for the stabilization of dynamic nonholonomic mechanic systems with unknown inertia parameters and disturbances. First, to facilitate the control design, the nonholonomic kinematic subsystem is transformed into a skew-symmetric form and the properties of the overall systems are discussed. Then, an adaptive NN controller is presented to guarantee the outputs of the dynamic subsystem (the inputs for the kinematic subsystem) to track the given auxiliary signals which are designed for the stabilization of kinematic subsystem. Neural networks are used to parameterize the unknown system functions and their weights are adaptively tuned. A robust term is added to suppress the approximation errors as well as the bounded unknown disturbances. The stability of the closed-loop system is proved using Lyapunov direct method. The effectiveness of the proposed control is validated through simulation on the control of a differential-drive mobile robot.