Adaptive output-constrained system with zone barrier Lyapunov function

It is essential to implement effective compliance control measures to ensure the safe and reliable operation of robots and automated systems. In this paper, zone barrier Lyapunov function is presented to the practical nonlinear system with adaptive fuzzy neural network control design. Output-constraint is considered by zone barrier Lyapunov function (zBLF), which is designed to enforce safety constraints and offer flexibility when the system states remain within a safe region of operation, even in the presence of nonlinear uncertainties. Adaptive fuzzy neural control is adopted to approximate the nonlinear uncertainties for practical stability analysis and design, which aims to adjust the control parameters online according to the system's behaviour. The fuzzy control based on zBLF symmetric output constraint is further extended to the asymmetric case. The output state converges to the trajectory and moves freely in a region around the origin, and then it is demonstrated the developed design method guarantees the boundedness of the states of a closed-loop system. Moreover, the system's residual set for each condition can be identified respectively. The simulation results on euler-lagrange system are to validate the effectiveness of the proposed scheme.