Adaptive neural network control for a class of low-triangular-structured nonlinear systems

In this paper, a class of unknown perturbed nonlinear systems is theoretically stabilized by using adaptive neural network control. The systems, with disturbances and nonaffine unknown functions, have low triangular structure, which generalizes both strict-feedback uncertain systems and pure-feedback ones. There do not exist any effective methods to stabilize this kind of systems. With some new conclusions for Nussbaum-Gain functions (NGF) and the idea of backstepping, semiglobal, uniformal, and ultimate boundedness of all the signals in the closed-loop is proved at equilibrium point. The two problems, control directions and control singularity, are well dealt with. The effectiveness of proposed scheme is shown by simulation on a proper nonlinear system.