Algorithms for improved fixed-time performance of Lyapunov-based economic model predictive control of nonlinear systems

Abstract

This work presents algorithms for improved fixed-time performance of Lyapunov-based economic model predictive control (LEMPC) of nonlinear systems. Unlike conventional Lyapunov-based model predictive control (LMPC) schemes which typically utilize a quadratic cost function and regulate a process at a steady-state, LEMPC designs very often dictate time-varying operation to optimize an economic (typically non-quadratic) cost function. The LEMPC algorithms proposed here utilize a shrinking prediction horizon with respect to fixed (but potentially large) operation period to ensure improved performance, measured by the desired economic cost, over conventional LMPC by solving auxiliary LMPC problems and incorporating appropriate constraints, based on the LMPC solution, in their formulations at various sampling times. The proposed LEMPC schemes also take advantage of a predefined Lyapunov-based explicit feedback law to characterize their stability region while maintaining the closed-loop system state in an invariant set subject to bounded process disturbances. The LEMPC algorithms are demonstrated through a nonlinear chemical process example.