Adaptive NN control of uncertain nonholonomic systems in chained form

In this paper, adaptive neural network (NN) control strategy is presented to solve the control problem of nonholonomic systems in a chained form with unknown virtual control coefficients and strong drift nonlinearities. The adaptive NN control laws are developed using state scaling and backstepping. The proposed control is free of control singularity problem. Adaptive control based switching strategy is adopted to overcome the uncontrollability problem associated with x₀(t₀) = 0. Uniform ultimate boundedness of all the signals in the closed-loop are guaranteed, and the system states are proven to converge to a small neighborhood of zero. The control performance of the closed-loop system is guaranteed by appropriately choosing the design parameters.