(568b) On Distributed Economic Model Predictive Control of Nonlinear Process Systems

In the context of control of large-scale nonlinear chemical process networks, an attractive control methodology is distributed model predictive control (DMPC) because it has the ability to control multiple-input multiple-output with input and state constraints while remaining computationally feasible to implement on-line through a distributed implementation of the computation (i.e., the computation is distributed to multiple processors) [1]-[2]. Recently, significant effort within the chemical process control community has focused on (centralized) economic model predictive control (e.g., [3]) which combines the advantages of a predictive control methodology with dynamic economic optimization by using a cost function that accounts for the process economics. Since EMPC may use a general (nonlinear) economic cost function and it may dictate a time-varying operation strategy, the on-line computation required to solve EMPC may be significant especially for large-scale process networks. Thus, distributed EMPC (DEMPC) may be one choice to significantly reduce the on-line computational burden. While early work on distributed EMPC (DEMPC) has shown some promising results in this direction [4]-[5], more work in this direction is in order including the development of DEMPC algorithms, rigorous theoretical stability analysis, and novel control loop decompositions methodologies tailored for DEMPC.

In this work, we focus on the development of sequential and iterative DEMPC for nonlinear chemical processes. The theoretical contribution of this work consists of three main parts. First, a novel control loop decomposition methodology on the basis of the process economics is developed. Second, two DEMPC schemes, designed with specific Lyapunov-based constraints [4], are formulated for sequential and iterative implementation, respectively. Third, a rigorous stability analysis of each of the DEMPC architectures is provided. While the stability analysis will be provided for general nonlinear process systems typically arising in chemical process industries, we tailor the formulation of the DEMPC algorithms with a specific focus on chemical processes that achieve better economic performance when operated in a time-varying fashion (e.g., periodic operation). The DEMPC architectures are demonstrated with a chemical process example previously studied in the context of periodic operation.

[1] Christofides PD, Liu J, Munoz de la Pena D. Networked and Distributed Predictive Control: Methods and Nonlinear Process Network Applications. Advances in Industrial Control Series. London, England: Springer-Verlag, 2011.
[2] Christofides PD, Scattolini R, Munoz de la Pena D, Liu J. Distributed model predictive control: A tutorial review and future research directions. Computers and Chemical Engineering. 2013;51:21-41.
[3] 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.
[4] Chen X, Heidarinejad M, Liu J, and Christofides PD. Distributed economic MPC: Application to a nonlinear chemical process network. Journal of Process Control. 2012;22:689-699.
[5] Lee J and Angeli D. Distributed cooperative nonlinear economic MPC. In: Proceedings of the 20th International Symposium on Mathematical Theory of Networks and Systems. Melbourne, Australia. 2012.