On fixed-time performance of Lyapunov-based economic model predictive control of nonlinear systems

This work presents an algorithm 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 algorithm proposed here utilizes 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. Closed-loop performance improvement is guaranteed by solving an auxiliary LMPC problem and incorporating appropriate constraints, based on the LMPC solution, in the LEMPC formulation at various sampling times. The proposed LEMPC scheme also takes advantage of a predefined Lyapunov-based explicit feedback law to characterize its stability region while maintaining the closed-loop system state in an invariant set. The performance of the LEMPC algorithm is demonstrated through a nonlinear chemical process example.