Economic model predictive control with time‐varying objective function for nonlinear process systems

Abstract

Economic model predictive control (EMPC) is a control scheme that combines real-time dynamic economic process optimization with the feedback properties of model predictive control (MPC) by replacing the quadratic cost function with a general economic cost function. Almost all the recent work on EMPC involves cost functions that are time invariant (do not explicitly account for time-varying process economics). In the present work, we focus on the development of a Lyapunov-based EMPC (LEMPC) scheme that is formulated with an explicitly time-varying economic cost function. First, the formulation of the proposed two-mode LEMPC is given. Second, closed-loop stability is proven through a theoretical treatment. Last, we demonstrate through extensive closed-loop simulations of a chemical process that the proposed LEMPC can achieve stability with time-varying economic cost as well as improve economic performance of the process over a conventional MPC scheme.

Economic and Distributed Model Predictive Control: Recent Developments in Optimization-Based Control

“…Lyapunov-based economic MPC schemes are, e.g., developed in [104], [106], [107]. Here, constraints based on a known control Lyapunov function are added to the repeatedly solved optimization problem to ensure that the system stays within a certain stability region or converges there.…”

Economic Model Predictive Control - A Review

“…Recent research works in [16,9,43] have shown strong interests and beneficial results. These works extend the previously developed stabilizing method of Lyapunov-based MPC [28] to EMPC.…”

“…An apparent difficulty around the pre-existing MPC theory for unreachable set-points is that the controller cost function was established as a Lyapunov function for the closed-loop system, while the cost function for the unreachable set-point problem may not Figure 1. RTO plus MPC vs. Economic MPC [9].…”

Theoretical advances on Economic Model Predictive Control with time-varying costs

“…Motivated by applications in areas where price variations are comparable in speed with process dynamics, the case of time-varying costs or parameter-varying costs were recently explored in Ellis & Christofides (2014). The method developed is a Lyapunov-based Economic MPC scheme which allows to guarantee boundedness of solutions as well as constraints satisfaction while attempting to optimize a time-varying cost functional.…”

“…As a matter of fact, in recent years, many efforts have been devoted to investigate Economic MPC variants allowing time-varying costs in several domains of application: management of energy in buildings (Touretzky & Baldea (2014); Ma et al (2014)), control of chemical plants (Ellis & Christofides (2014)) and supervision of distribution networks, such as water networks ), power grids (Hovgaard et al (2010); Cole et al (2014); Adeodu & Chmielewski (2013),) gas networks, etc (Gopalakrishnan & Biegler (2013)). Other Economic MPC approaches dealing either time-varying cost or cyclic plant operations from a theoretical perspective can be found in Ferramosca et al (2014); Limon et al (2014);Huang et al (2012).…”