Distributed nonlinear model predictive control through accelerated parallel ADMM

Alternating direction method of multipliers (ADMM), as a powerful distributed optimization algorithm, provides a framework for distributed model predictive control (MPC) for nonlinear process systems based on local subsystem model information. However, the practical application of classical ADMM is largely limited by the high computational cost caused by its slow (linear) rate of convergence and non-parallelizability. In this work, we combine a recently developed multi-block parallel ADMM algorithm with a Nesterov acceleration technique into a fast ADMM scheme, and apply it to the solution of optimal control problems associated with distributed nonlinear MPC. A benchmark chemical process is considered for a case study, which demonstrates a significant reduction of computational time and communication effort compared to non-parallel and non-accelerated ADMM counterparts.

[1]  C. Ocampo‐Martinez,et al.  Partitioning Approach oriented to the Decentralised Predictive Control of Large-Scale Systems , 2011 .

[2]  Colin Neil Jones,et al.  A Parametric Nonconvex Decomposition Algorithm for Real-Time and Distributed NMPC , 2016, IEEE Transactions on Automatic Control.

[3]  Zhi-Quan Luo,et al.  On the linear convergence of the alternating direction method of multipliers , 2012, Mathematical Programming.

[4]  Richard G. Baraniuk,et al.  Fast Alternating Direction Optimization Methods , 2014, SIAM J. Imaging Sci..

[5]  Victor M. Zavala,et al.  Large-scale nonlinear programming using IPOPT: An integrating framework for enterprise-wide dynamic optimization , 2009, Comput. Chem. Eng..

[6]  Bingsheng He,et al.  On Full Jacobian Decomposition of the Augmented Lagrangian Method for Separable Convex Programming , 2015, SIAM J. Optim..

[7]  Panagiotis D. Christofides,et al.  Distributed model predictive control: A tutorial review and future research directions , 2013, Comput. Chem. Eng..

[8]  Moritz Diehl,et al.  CasADi: a software framework for nonlinear optimization and optimal control , 2018, Mathematical Programming Computation.

[9]  Prodromos Daoutidis,et al.  Control‐relevant decomposition of process networks via optimization‐based hierarchical clustering , 2016 .

[10]  Prodromos Daoutidis,et al.  Optimal decomposition for distributed optimization in nonlinear model predictive control through community detection , 2018, Comput. Chem. Eng..

[11]  Fu Lin,et al.  Flexibility characterization of multi-zone buildings via distributed optimization , 2018, 2018 Annual American Control Conference (ACC).

[12]  João M. F. Xavier,et al.  Distributed Optimization With Local Domains: Applications in MPC and Network Flows , 2013, IEEE Transactions on Automatic Control.

[13]  Prodromos Daoutidis,et al.  Network decomposition for distributed control through community detection in input–output bipartite graphs , 2018 .

[14]  Wotao Yin,et al.  Global Convergence of ADMM in Nonconvex Nonsmooth Optimization , 2015, Journal of Scientific Computing.

[15]  Lorenz T. Biegler,et al.  Parallel cyclic reduction decomposition for dynamic optimization problems , 2019, Comput. Chem. Eng..

[16]  James B. Rawlings,et al.  Postface to “ Model Predictive Control : Theory and Design ” , 2012 .

[17]  Y. Nesterov.  A method for solving the convex programming problem with convergence rate O(1/k^2) , 1983 .

[18]  Prodromos Daoutidis,et al.  Community-based synthesis of distributed control architectures for integrated process networks , 2017 .

[19]  Stephen P. Boyd,et al.  Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..

[20]  Zhi-Quan Luo,et al.  Convergence analysis of alternating direction method of multipliers for a family of nonconvex problems , 2015, ICASSP.

[21]  Prodromos Daoutidis,et al.  Impact of Decomposition on Distributed Model Predictive Control: A Process Network Case Study , 2017 .

[22]  Panagiotis D. Christofides,et al.  Sequential and Iterative Architectures for Distributed Model Predictive Control of Nonlinear Process Systems , 2010 .

[23]  Prodromos Daoutidis,et al.  Graph representation and decomposition of ODE/hyperbolic PDE systems , 2017, Comput. Chem. Eng..

[24]  Wotao Yin,et al.  Parallel Multi-Block ADMM with o(1 / k) Convergence , 2013, Journal of Scientific Computing.

[25]  Shiqian Ma,et al.  On the Global Linear Convergence of the ADMM with MultiBlock Variables , 2014, SIAM J. Optim..

[26]  Niels Kjølstad Poulsen,et al.  Distributed Model Predictive Control for Smart Energy Systems , 2016, IEEE Transactions on Smart Grid.

[27]  Karl Henrik Johansson,et al.  Distributed MPC Via Dual Decomposition and Alternative Direction Method of Multipliers , 2012, ArXiv.

[28]  Stephen J. Wright,et al.  Cooperative distributed model predictive control , 2010, Syst. Control. Lett..

[29]  Vladimir Pavlovic,et al.  Fast ADMM Algorithm for Distributed Optimization with Adaptive Penalty , 2015, AAAI.

[30]  Prodromos Daoutidis,et al.  Reprint of: Optimal decomposition for distributed optimization in nonlinear model predictive control through community detection , 2018, Comput. Chem. Eng..