Zone Barrier Lyapunov Functions for State Constrained Systems
Xiaoling Liang, Shuzhi Sam Ge
Abstract
This paper has been used to investigate the zone barrier Lyapunov function for state-constrained systems. This study provides control designs in the strict feedback form for nonlinear systems to accomplish full-state constraints and partial-state constraints. To keep states from breaking the rules, zone barrier Lyapunov functions (zBLFs) are developed, which increase to infinity once the inputs reach some boundaries. The limitations are not exceeded in the closed-loop system by assuring the boundedness of the barrier function and the freedom is offered for the states in the predefined zone. When faced with all state constraints, we utilize zBLFs at every stage of the design process. Further, only a few states are constrained, we modify the design procedure so that zBLFs are applied only up to the stage where the highest-order state is under constraint. Sufficient conditions are specified to ensure feasibility, and that all closed-loop signals are bounded if specific criteria on initial states are met. Then the main results are extended to the case of the situation where only some of the states require restrictions. Numerical simulations and hardware experiments are provided to verify the validity of the obtained theoretical results.