(569a) On the Role of Constraints in Economic Model Predictive Control

Economic model predictive control (EMPC) has recently attracted substantial attention within the chemical process control and energy systems communities because of its unique ability to control nonlinear processes/systems while reconciling process economic optimization and process control (e.g., [1]-[4]; see, also, the recent review [5] for comprehensive reference list of recent papers on EMPC). Unlike tracking model predictive control which uses a quadratic stage cost, EMPC uses a general, user-defined stage cost that reflects the process economics. Owing to the generality of the stage cost, achieving recursive feasibility of the EMPC optimization problem, closed-loop stability, and certain guarantees on closed-loop economic performance properties do not generally follow by applying EMPC unless additional conditions are satisfied (e.g., additional constraints are imposed on the EMPC optimization problem and/or a sufficiently long prediction horizon be used).

A brief overview of EMPC methods is provided with a particular focus on the role of constraints imposed in the EMPC optimization problem to address recursive feasibility, closed-loop stability, and closed-loop performance. Three main types of constraints are considered including terminal equality constraints, terminal region constraints, and constraints designed via Lyapunov-based techniques. An explanation of the motivation behind each type of constraint is provided. Additionally, the conditions that must be satisfied to yield the three closed-loop properties (feasibility, stability, and performance) are presented and explained. A well-known chemical engineering example, a non-isothermal CSTR with a second-order reaction, is used to illustrate effectiveness and theoretical performance properties of time-varying operation to improve closed-loop economic performance compared to steady-state operation and to demonstrate the impact of economically motivated constraints on optimal operation.

[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] Huang R, Harinath E, Biegler LT. Lyapunov stability of economically oriented NMPC for cyclic processes. Journal of Process Control. 2011;21:501-509.
[4] Heidarinejad M, Liu J, Christofides PD. Economic model predictive control of nonlinear process systems using Lyapunov techniques. AIChE Journal. 2012;58:855-870.
[5] Ellis M, Durand H, Christofides PD. A tutorial review of economic model predictive control methods. Journal of Process Control, 2014;24:1156--1178.