(371j) Handling Bounded and Unbounded Unsafe Sets in Control Lyapunov-Barrier Function-Based Model Predictive Control of Nonlinear Processes

Authors: 
Wu, Z., University of California, Los Angeles
Christofides, P. D., University of California, Los Angeles
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 [1,2]. In this work, we develop 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 [3]. Specifically, in the presence of a bounded unsafe region embedded within the closed-loop system stability region, the CLBF-based model predictive control (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.

On the other hand, if CLBF is incorporated in the design of economic model predictive control (EMPC) to address process control tasks integrated with dynamic economic optimization of the process [4,5], simultaneous closed-loop stability and process operational safety are ensured for both bounded and unbounded unsafe region because the closed-loop system is not required to converge to the origin under EMPC. The application of the proposed CLBF-MPC and CLBF-EMPC methods are demonstrated through a chemical process example with a bounded and an unbounded unsafe region, respectively.

[1] Wieland, P., and Allgöwer, F. Constructive safety using control barrier functions. IFAC Proceedings Volumes, 40, 462-467, 2007.

[2] Romdlony, M. Z., and Jayawardhana, B. Stabilization with guaranteed safety using control Lyapunov–barrier function. Automatica, 66, 39-47, 2016.

[3] Wu, Z., and Christofides, P. D. Handling Bounded and Unbounded Unsafe Sets in Control Lyapunov-Barrier Function-Based Model Predictive Control of Nonlinear Processes. Chem. Eng. Res. & Des., 143, 140-149, 2019.

[4] Ellis M, Durand H, Christofides, P. D. A tutorial review of economic model predictive control methods. Journal of Process Control. 2014, 24:1156-1178.

[5] Wu, Z., Durand, H. and Christofides, P. D. Safe Economic Model Predictive Control of Nonlinear Systems. Syst. & Contr. Lett., 118, 69-76, 2018.