On Impact of Unsafe Set Structure in Control Lyapunov-Barrier Function-Based Model Predictive Control

In this work, we developed Control Lyapunov-Barrier functions for two types of unsafe regions (i.e., bounded and unbounded sets) to solve the problem of stabilization of nonlinear systems with guaranteed safety. Specifically, discontinuous control actions are required to handle potential stationary points (except the origin) for Control Lyapunov-Barrier function in the presence of a bounded unsafe region embedded within the closed-loop system stability region. Subsequently, the CLBF-MPC is developed by incorporating CLBF-based constraints to guarantee closed-loop stability with safety for both bounded and unbounded unsafe regions. The application of the proposed CLBF-MPC method is demonstrated through a chemical process example with a bounded and an unbounded unsafe region, respectively.