420816 Closed-Loop Average Economic Performance Under Real-Time Economic Model Predictive Control

Thursday, November 12, 2015: 3:15 PM
Salon D (Salt Lake Marriott Downtown at City Creek)
Matthew Ellis, Chemical and Biomolecular Engineering, University of California, Los Angeles, Los Angeles, CA and Panagiotis D. Christofides, Department of Chemical and Biomolecular Engineering and Department of Electrical Engineering, University of California, Los Angeles, Los Angeles, CA

Economic model predictive control (EMPC), an optimal control-based feedback control methodology, unites process control and economic process optimization into an integrated framework (e.g., [1]-[5]). The main objective of applying EMPC to control a chemical process over tracking model predictive control (TMPC) is to achieve improved closed-loop economic performance. It is well-known that closed-loop performance under EMPC without specific terminal conditions is not ensured in general. To address this problem, terminal conditions may be used. In [1], the asymptotic average economic performance under EMPC formulated with an equality terminal constraint was shown to be at least as good as the economic performance at the economically optimal steady-state. Other EMPC system have been proposed utilizing an equality terminal constraint or terminal region constraint which are designed on the basis of the optimal steady-state (e.g., [2]). Nevertheless, when terminal constraints are imposed in the EMPC optimization problem, recursive feasibility for systems with plant-model mismatch may not be ensured. On the other hand, when no terminal conditions are imposed in the EMPC problem, a sufficiently long prediction horizon is typically required for some guarantees on closed-loop performance under EMPC [3]. The use of a long prediction horizon may make EMPC computationally intractable for use in real-time operation. Moreover, an important issue from a practical stand-point for EMPC is real-time computation time. When the computation time is significant, closed-loop operation and/or performance degradation may occur.

In this work, a Lyapunov-based EMPC (LEMPC) scheme for nonlinear process systems is designed leveraging an auxiliary stabilizing control law and addressing real-time computation delay through an event-triggered implementation strategy. In particular, an auxiliary control law (e.g., TMPC or Lyapunov-based control law) is designed to stabilize a process at the economically optimal steady-state. The process model with the auxiliary control law are used to predict the solution of the system under the auxiliary control law over a finite-time horizon. Motivated by the desire to ensure economic performance improvement under EMPC compared to under the auxiliary control law, the computed solution is utilized in the LEMPC scheme as a terminal constraint. This type of terminal constraint is similar to that proposed in [4] for use in EMPC. To account for real-time computational time, the real-time implementation strategy for LEMPC proposed in [5] is extended to the proposed LEMPC with the terminal constraint designed on the basis of the solution of the system under the auxiliary control law. Recursive feasibility of the proposed LEMPC scheme, closed-loop stability, and finite-time and asymptotic average economic closed-loop performance are analyzed. The scheme is applied to a chemical process example to demonstrate the theoretical properties of the proposed LEMPC scheme.

[1] Angeli D, Amrit R, Rawlings JB. On average performance and stability of economic model predictive control. IEEE Transactions on Automatic Control. 2012;57:1615-1626.
[2] Amrit R, Rawlings JB, Angeli D. Economic optimization using model predictive control with a terminal cost. Annual Reviews in Control. 2011;35:178-186.
[3] Grune L. Economic receding horizon control without terminal constraints. Automatica. 2013;49:725--734.
[4] Ellis M, Christofides PD. On finite-time and infinite-time cost improvement of economic model predictive control for nonlinear systems. Automatica. 2014;50:2561--2569.
[5] Ellis M, Christofides PD. Real-time economic model predictive control of nonlinear process systems. AIChE Journal. 2015;61:555--571.

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