Barrier Lyapunov functions

A barrier Lyapunov functions (BLFs)-based localized adaptive neural network (NN) control is proposed for a class of uncertain nonlinear systems with state and asymmetric control constraints to track the reference trajectory. To handle system constraints, BLFs are used in the backstepping procedure, and the control input is considered as an extended state variable. This extends current research on BLFs-based control for systems with state and output constraints to systems with state and asymmetric control constraints. A locally weighted learning NN with projection modification is designed to estimate and compensate for the system uncertainty. The use of projection modification ensures the NN estimator is contained in a given bounded area and prevents the absolute value of NN output from being near to or larger than the bound of the tracking error. The feasibility and effectiveness of the proposed control have been demonstrated by formal proof and simulation results