Handling bounded and unbounded unsafe sets in Control Lyapunov-Barrier function-based model predictive control of nonlinear processes

Abstract

Control Lyapunov-Barrier function (CLBF) has been used to design controllers for nonlinear systems subject to input constraints to ensure closed-loop stability and process operational safety simultaneously. 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 process operational safety. Specifically, in the presence of a bounded unsafe region embedded within the closed-loop system stability region, the CLBF-MPC is developed by incorporating CLBF-based constraints and discontinuous control actions at potential stationary points (except the origin) to guarantee the convergence to the origin (i.e., closed-loop stability) and the avoidance of unsafe region (i.e., process operational safety). In the case of unbounded unsafe sets, closed-loop stability with safety is readily guaranteed under the CLBF-MPC since the origin is the unique stationary point in state-space. The application of the proposed CLBF-MPC method is demonstrated through a chemical process example with a bounded and an unbounded unsafe region, respectively.