Distributed Model Predictive Control with suboptimality and stability guarantees
Published 1 December 2010Open access
Pontus Giselsson, Anders Rantzer
Citations120
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
A stopping criterion for the DMPC scheme is presented that can be locally verified by each node and that guarantees closed loop suboptimality above a pre-specified level and asymptotic stability of the interconnected system.
Abstract
Theory for Distributed Model Predictive Control (DMPC) is developed based on dual decomposition of the convex optimization problem that is solved in each time sample. The process to be controlled is an interconnection of several subsystems, where each subsystem corresponds to a node in a graph. We present a stopping criterion for the DMPC scheme that can be locally verified by each node and that guarantees closed loop suboptimality above a pre-specified level and asymptotic stability of the interconnected system.
Keywords
Engineering
AutomaticaConstrained model predictive control: Stability and optimality
8,395 Citations2000D.Q. Mayne, James B. Rawlings +2 more
This review focuses on model predictive control of constrained systems, both linear and nonlinear, and distill from an extensive literature essential principles that ensure stability to present a concise characterization of most of the model predictive controllers that have been proposed in the literature.
Computers & Chemical EngineeringModel predictive control: past, present and future
2,297 Citations1999Manfred Morari, Jay H. Lee
IEEE Control SystemsDistributed model predictive control
949 Citations2002Eduardo Camponogara, Dong Jia +2 more
Results for distributed model predictive control are presented, focusing on the coordination of the optimization computations using iterative exchange of information and the stability of the closed-loop system when information is exchanged only after each iteration.
EconometricaThe Decomposition Algorithm for Linear Programs
747 Citations1961George B. Dantzig, Philip Wolfe
Model predictive control in the process industry
595 Citations1995Eduardo F. Camacho, Carlos A. Bordons
IEEE Transactions on Automatic ControlDistributed Receding Horizon Control of Dynamically Coupled Nonlinear Systems
381 Citations2007William B. Dunbar
A distributed RHC algorithm is presented for dynamically coupled nonlinear systems that are subject to decoupled input constraints and the theoretical conditions for feasibility and stability are shown to be satisfied for a set of coupled Van der Pol oscillators that model a walking robot experiment.
Journal of the Operational Research SocietyControl and Coordination in Hierarchical Systems
351 Citations1981John R. Beaumont
This book presents the applied theory of control and cooordination in hierarchical systems which are those where decision making has been divided in a certain way to concentrate on various aspects of optimal control in large scale systems.
IEEE Transactions on Automatic ControlRelaxing Dynamic Programming
331 Citations2006B. Lincoln, Anders Rantzer
This paper introduces a method to reduce the complexity by relaxing the demand for optimality, which is applied to a partially observable Markov decision problem (POMDP).
Stability and optimality of distributed model predictive control
295 Citations2006Aswin N. Venkat, James B. Rawlings +1 more
This article extends existing concepts in linear model predictive control to a unified, theoretical framework for distributed MPC with guaranteed nominal stability and performance properties and addresses Kalman filtering framework for state estimation.
SIAM Journal on Control and OptimizationAnalysis and Design of Unconstrained Nonlinear MPC Schemes for Finite and Infinite Dimensional Systems
183 Citations2009Lars Grüne
The insight obtained from the numerical solution of this problem is derived and design guidelines for nonlinear MPC schemes which guarantee stability of the closed loop for small optimization horizons are derived.
IEEE Transactions on Automatic ControlOn the Infinite Horizon Performance of Receding Horizon Controllers
182 Citations2008Lars Grüne, Anders Rantzer
This paper provides a method to quantify the performance degradation that comes with this approximation of fading horizon control.
SIAM Journal on Control and OptimizationOptimization with an Auxiliary Constraint and Decomposition
145 Citations1990Guy Cohen, Bernadette Miara
Research Repository (Delft University of Technology)Multi-agent model predictive control with applications to power networks
133 Citations2007Rudy R. Negenborn
This PhD thesis proposes several novel control techniques for the control of transportation networks based on a combination of ideas from the fields of multi-agent systems and model predictive control.
AutomaticaApplied mathematics in water supply network management
61 Citations1993Pierre Carpentier, Guy Cohen
This paper tells the story of about 10 years of involvement of the research group in the application of mathematical techniques for the management of complex water supply networks: optimal control over 24-hr periods, and state estimation and leak detection.
Application of the proximal center decomposition method to distributed model predictive control
42 Citations2008Ion Necoara, Dang Doan +1 more
A dual-based decomposition method to solve distributed model predictive control problems for coupled dynamical systems but with decoupled cost and constraints and it is shown that the centralized MPC problem can be recast as a separable convex problem for which the method can be applied.
2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)Temporal Lagrangian decomposition of model predictive control for hybrid systems
26 Citations2004Marco Beccuti, Tobias Geyer +1 more
Given a model predictive control problem for a hybrid system in the mixed logical dynamical (MLD) framework, a temporal decomposition scheme is proposed that efficiently derives the control actions by performing Lagrangian decomposition on the prediction horizon.
Adaptive Nonlinear Model Predictive Control with suboptimality and stability guarantees
18 Citations2010Pontus Giselsson
Theory for Adaptive Nonlinear Model Predictive Control is developed based on the relaxed dynamic programming inequality, which provides guarantees for asymptotic stability and closed loop suboptimality above a certain pre-specified level.