Nonlinear Control Design Based on Zone Barrier Lyapunov Function

This paper investigates the control design for nonlinear systems with output constraint, according to a safe set from mathematical understanding or zone stability from an engineering point of view, and the corresponding zone Barrier Lyapunov Function (zBLF) stability analysis. The novel constraint function is provided to allow the output state to travel freely in the predefined zone meanwhile not transgress the barrier area. To articulate the area-keeping problem, we first propose the zone stability to a second SISO nonlinear system. Next, zBLF in asymmetric form is developed into a class of nonlinear systems in the strict feedback form. The stability analysis of the zone Barrier Lyapunov function is to ensure that the output does not break free of the restricted constraint while simultaneously ensuring that the states remain free within the admissible set. As a result, control theory expands its range of applications and contributes to its application development. The actual system does not need to do additional work to achieve the state constraint. Finally, the numerical example is conducted to illustrate the zBLF features and further explorations of the merits are carried out to showcase the effectiveness.