(148h) Real-Time Economic Model Predictive Control of Nonlinear Systems

Economic model predictive control (EMPC) is a control methodology that unites feedback control and real-time process economic optimization (e.g., [1]-[5]). The optimization problem of EMPC consists of three main parts: an objective function that accounts for the process economics, process constraints including state and inputs constraints and other constraints like stability and performance constraints, and a dynamic model to predict the future evolution of the process (thus, be able to select the optimal input profile with respect to the economics over an operating horizon). Regardless of the implementation strategy of EMPC (i.e., centralized, distributed, or hierarchical), the computation time required to solve the optimization-based controller is non-zero in practice. The computation time may be significant or insignificant depending on the time constants of the process dynamics. When the computation time is significant, using an EMPC that does not account for the delay caused by the computation time may lead to unstable closed-loop operation and/or performance degradation. However, no theoretical work on the closed-loop stability properties of EMPC accounting for the computation delay as been completed.

To this end, EMPC for real-time implementation is considered in this work. Specifically, a Lyapunov-based EMPC (LEMPC) [4] explicitly accounting for computational delays is proposed. From a performance perspective, it may be advantageous to provide the EMPC with knowledge of the computation delay when they are significant. Thus, the EMPC is formulated with a model that treats the computational delay as an input time-delay and the average computation time is used to model the input time-delay. From a stability perspective, there is a (theoretical) maximum amount of time that the optimization problem solver may spend in computation and must return a control action by this maximum amount of time to ensure closed-loop stability. A rigorous bound on the maximum amount of computation time to ensure closed-loop is derived. The bound will be used to force the solver to return a control action by the maximum computational time required for stability. By the design of the LEMPC, the returned control action, which may be returned before the solver converges to a (local) solution, is guaranteed to be stabilizing. The proposed LEMPC is demonstrated on a chemical process example to show that closed-loop stability can be maintained in the presence of computation delay.

[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, in press.