Distributed predictive control with minimization of mutual disturbances

Abstract In this paper, a distributed model predictive control scheme is proposed for linear, time-invariant dynamically coupled systems. Uniquely, controllers optimize state and input constraint sets, and exchange information about these–rather than planned state and control trajectories–in order to coordinate actions and reduce the effects of the mutual disturbances induced via dynamic coupling. Mutual disturbance rejection is by means of the tube-based model predictive control approach, with tubes optimized and terminal sets reconfigured on-line in response to the changing disturbance sets. Feasibility and exponential stability are guaranteed under provided sufficient conditions on non-increase of the constraint set parameters.

[1]  Eduardo F. Camacho,et al.  A coalitional control scheme with applications to cooperative game theory , 2014 .

[2]  Rolf Findeisen,et al.  Contract-based Predictive Control of Distributed Systems with Plug and Play Capabilities , 2015 .

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

[4]  David Q. Mayne,et al.  Model predictive control: Recent developments and future promise , 2014, Autom..

[5]  Jan M. Maciejowski,et al.  Predictive control : with constraints , 2002 .

[6]  David Q. Mayne,et al.  Robust model predictive control of constrained linear systems with bounded disturbances , 2005, Autom..

[7]  Pablo R. Baldivieso Monasterios,et al.  Distributed MPC with minimization of mutual disturbance sets , 2016, 2016 American Control Conference (ACC).

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

[9]  Paul A. Trodden,et al.  Distributed model predictive control of linear systems with persistent disturbances , 2010, Int. J. Control.

[10]  Torkel Glad,et al.  Reference Tracking MPC Using Dynamic Terminal Set Transformation , 2014, IEEE Transactions on Automatic Control.

[11]  S. Joe Qin,et al.  A survey of industrial model predictive control technology , 2003 .

[12]  Marcello Farina,et al.  Block-wise discretization accounting for structural constraints , 2013, Autom..

[13]  Alexandre Trofino,et al.  Sufficient LMI conditions for output feedback control problems , 1999, IEEE Trans. Autom. Control..

[14]  Paul A. Trodden A One-Step Approach to Computing a Polytopic Robust Positively Invariant Set , 2016, IEEE Transactions on Automatic Control.

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

[16]  K. T. Tan,et al.  Linear systems with state and control constraints: the theory and application of maximal output admissible sets , 1991 .

[17]  Nimrod Megiddo,et al.  Linear Programming in Linear Time When the Dimension Is Fixed , 1984, JACM.

[18]  Eduardo F. Camacho,et al.  MPC for tracking piecewise constant references for constrained linear systems , 2008, Autom..

[19]  Marcello Farina,et al.  Plug-and-play model predictive control based on robust control invariant sets , 2012, Autom..

[20]  Gilles Millerioux,et al.  MPC tracking under time-varying polytopic constraints for real-time applications , 2014, 2014 European Control Conference (ECC).

[21]  Paul A. Trodden,et al.  Cooperative distributed MPC of linear systems with coupled constraints , 2013, Autom..

[22]  Antonio Ferramosca,et al.  MPC for tracking with optimal closed-loop performance , 2009, Autom..

[23]  David Q. Mayne,et al.  Optimized robust control invariance for linear discrete-time systems: Theoretical foundations , 2007, Autom..

[24]  J. M. Maestre,et al.  Distributed Model Predictive Control: An Overview and Roadmap of Future Research Opportunities , 2014, IEEE Control Systems.

[25]  Stefano Riverso,et al.  Tube-based distributed control of linear constrained systems , 2012, Autom..

[26]  Jonathan P. How,et al.  Robust distributed model predictive control , 2007, Int. J. Control.

[27]  Bart De Schutter,et al.  Optimal Coordination of a Multiple HVDC Link System Using Centralized and Distributed Control , 2013, IEEE Transactions on Control Systems Technology.

[28]  Edward N. Hartley,et al.  Reconfigurable predictive control for redundantly actuated systems with parameterised input constraints , 2014, Syst. Control. Lett..

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

[30]  Basil Kouvaritakis,et al.  Equi-normalization and exact scaling dynamics in homothetic tube model predictive control , 2013, Syst. Control. Lett..

[31]  David Q. Mayne,et al.  Invariant approximations of the minimal robust positively Invariant set , 2005, IEEE Transactions on Automatic Control.

[32]  Peter Gritzmann,et al.  Minkowski Addition of Polytopes: Computational Complexity and Applications to Gröbner Basis , 1993, SIAM J. Discret. Math..

[33]  Marcello Farina,et al.  Distributed predictive control: A non-cooperative algorithm with neighbor-to-neighbor communication for linear systems , 2012, Autom..

[34]  Fabio A. de Almeida,et al.  Reference Management for Fault-Tolerant Model Predictive Control , 2010 .