Control of Nonlinear System with State-Constraints using Barrier Lyapunov Function and Backstepping Method

Abstract

© 2018 SERSC Australia. This paper presents the application of Barrier Lyapunov Function (BLF) and backstepping technique to stabilize a nonlinear dynamic system with state-constraints. A barrier function, which limits the region of Lyapunov function candidate, is utilized to design an algorithm that stabilizes each subsystem. Then, a backstepping approach is applied to generate control law that stabilizes the whole system recursively. Using the control law derived from this combination, the origin of state-constrained system is asymptotically stable for all initial conditions within the respective constraints range. For validation, the performance of this proposed control law is demonstrated by simulation, where all of the state trajectories converge to the origin.