(709c) Accelerating Distributed MPC Via Facet Properties: Faster Computation with Lower Communication Overhead

Cooperative Distributed Model Predictive Control (DiMPC) architecture [1] employs local MPC controllers to control individual subsystems, exchanging information with each other through an iterative procedure to enhance overall control performance compared to the decentralized architecture [2]. However, this method can result in high communication burden between the controllers and increased computational costs. To reduce the computation time, previous studies improved convergence rate per iteration [3, 4] or accelerated solution time of optimal control problems by employing explicit-MPC [5] in the DiMPC framework. To reduce both computation and communication load, a multiparametric (mp) programming [6] based iteration free cooperative DiMPC (IF-mpDiMPC) method was proposed by Saini et al. [7]. The framework leverages mp programming to compute explicit control laws [8]—defined by critical regions—offline for each subsystem and simultaneously solve them, enabling real-time control without iterative control data exchanges.

We propose a novel facet-based iteration-free method that builds on the IF-mpDiMPC framework to achieve greater computational efficiency. The method solves mp programming-based explicit control laws simultaneously as systems of linear equations while limiting the solution space through reduced combinations. By leveraging the geometric properties of critical regions in mp solutions, the proposed approach restricts the online search for optimal control inputs to the current critical region and its facet-sharing neighbors. Identifying pairs of facet-sharing critical regions requires solving multiple linear programs [9], although this computation can be performed offline, after the solution of the mp programs, avoiding real-time overhead. Simulation results demonstrate a 41% reduction in average computation time over prior iteration-free approaches, while achieving centralized-level control performance.

References:
[1] Stewart, B.T., Venkat, A.N., Rawlings, J.B., Wright, S.J. and Pannocchia, G., 2010. Cooperative distributed model predictive control. Systems & Control Letters, 59(8), pp.460-469.

[2] Christofides, P.D., Scattolini, R., De La Pena, D.M. and Liu, J., 2013. Distributed model predictive control: A tutorial review and future research directions. Computers & Chemical Engineering, 51, pp.21-41.

[3] Wang, J. and Yang, Y., 2022. An improved iterative solution for cooperative distributed MPC. Automatica, 140, p.110155.

[4] Cai, X., Tippett, M.J., Xie, L. and Bao, J., 2014. Fast distributed MPC based on active set method. Computers & chemical engineering, 71, pp.158-170.

[5] Saini, R.S., Pappas, I., Avraamidou, S. and Ganesh, H.S., 2023. Noncooperative distributed model predictive control: A multiparametric programming approach. Industrial & Engineering Chemistry Research, 62(2), pp.1044-1056.

[6] Pappas, I., Kenefake, D., Burnak, B., Avraamidou, S., Ganesh, H.S., Katz, J., Diangelakis, N.A. and Pistikopoulos, E.N., 2021. Multiparametric programming in process systems engineering: Recent developments and path forward. Frontiers in Chemical Engineering, 2, p.620168.

[7] Saini, R.S., Brahmbhatt, P.R., Avraamidou, S. and Ganesh, H.S., 2024. Iteration-Free Cooperative Distributed MPC through Multiparametric Programming. arXiv preprint arXiv:2411.14319.

[8] Bemporad, A., Morari, M., Dua, V. and Pistikopoulos, E.N., 2002. The explicit linear quadratic regulator for constrained systems. Automatica, 38(1), pp.3-20.

[9] Airan, A., Bhushan, M. and Bhartiya, S., 2016. Linear machine solution to point location problem. IEEE Transactions on Automatic Control, 62(3), pp.1403-1410.