Adaptive Regulation for a Class of Non-Affine Systems using Neural Network Backstepping with Tuning Functions

A backstepping based neural synthesis method is proposed to stabilize a class of non-affine systems, that include non-minimum phase systems as well. The method describes the class of systems in normal form, and uses two neural networks, while previous backstepping methods introduce a neural networks at each backward step. The neural weights are updated using tuning functions, and nonlinear damping terms prevent the functional reconstruction error from propagating to the next backward step. The method does not rely on a fixed-point assumption, nor does it assume that the time derivative of the control effectiveness is bounded (an assumption that is commonly employed when using the mean value theorem). All the signals of the closed-loop system are shown to be uniformly ultimately bounded. Simulation results illustrate the approach