Tangent Barrier Lyapunov Functions for the Control of Output-Constrained Nonlinear Systems

In this paper, we present a systematic control design for strict-feedback nonlinear systems with output constraints using tangent Barrier Lyapunov Functions (BLFs-Tan). Both symmetric and asymmetric BLF-Tan based backstepping control design methods are developed. It is proved that with the proposed approach and Lyapunov synthesis, the output constraints are not violated, all signals in the closed-loop systems are bounded, and asymptotical tracking is achieved. Through the simulation, we also perform a comparison study between BLF-Tan and the logarithmic BLF (BLF-Log) to illustrate the difference in control performance, and show that the performance of asymmetric BLF-Tan based controller depends on the position of initial tracking error with respect to the transformed constraint boundary.