Cooperative Distributed MPC Using the Alternating Direction Multiplier Method

Abstract We consider cooperative distributed model predictive control of a linear, time-invariant, discrete-time plant, which consists of coupled subsystems. The cooperating controllers minimize a quadratic cost criterion subject to input and state constraints. We outline two approaches for such distributed controllers using the alternating direction multiplier method, which allows to obtain convergence guarantees. We outline suitable stability criterions and illustrate the applicability and performance of the proposed methods by a simple example.

[1]  Bart De Schutter,et al.  An improved distributed version of Han's method for distributed MPC of canal systems , 2010 .

[2]  Yasushi Hada,et al.  Constrained Model Predictive Control , 2006 .

[3]  J. Rawlings,et al.  The stability of constrained receding horizon control , 1993, IEEE Trans. Autom. Control..

[4]  Martin Guay,et al.  Coordination of Distributed Model Predictive Controllers for Constrained Dynamic Processes* *This work is supported by Natural Sciences and Engineering Research Council of Canada (NSERC) and Alberta Ingenuity. , 2009 .

[5]  Eduardo F. Camacho,et al.  Constrained Model Predictive Control , 2007 .

[6]  John N. Tsitsiklis,et al.  Parallel and distributed computation , 1989 .

[7]  Stephen J. Wright,et al.  Application of Interior-Point Methods to Model Predictive Control , 1998 .

[8]  Manfred Morari,et al.  Distributed synthesis and control of constrained linear systems , 2012, 2012 American Control Conference (ACC).

[9]  Anders Rantzer,et al.  Distributed Model Predictive Control with suboptimality and stability guarantees , 2010, 49th IEEE Conference on Decision and Control (CDC).

[10]  J. Primbs,et al.  Constrained finite receding horizon linear quadratic control , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[11]  Wolfgang Marquardt,et al.  Distributed Model-Predictive Control Driven by Simultaneous Derivation of Prices and Resources , 2011 .

[12]  Bart De Schutter,et al.  Distributed model predictive control of irrigation canals , 2009, Networks Heterog. Media.

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

[14]  F. Allgöwer,et al.  A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability , 1997 .

[15]  David Q. Mayne,et al.  Constrained model predictive control: Stability and optimality , 2000, Autom..

[16]  Kanya Tanaka,et al.  Decentralized model predictive control via dual decomposition , 2008, 2008 47th IEEE Conference on Decision and Control.

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

[18]  Riccardo Scattolini,et al.  Architectures for distributed and hierarchical Model Predictive Control - A review , 2009 .