Distributed Optimization for MPC of Linear Networks With Uncertain Dynamics

A linear dynamic network consists of a directed graph whose nodes are subsystems and whose arcs define dynamic couplings. Subsystem states evolve depending on the local and upstream control signals according to uncertain dynamics. Dynamic networks can serve as models for geographically distributed systems such as traffic networks and petrochemical plants. This technical note develops a distributed algorithm to operate a linear dynamic network with a network of agents that implement a distributed model predictive control strategy. Based on subgradient optimization to handle nondifferentiability, the distributed algorithm is shown to converge to an optimal solution.

[1]  Bart De Schutter,et al.  Multi-agent model predictive control for transportation networks: Serial versus parallel schemes , 2008, Eng. Appl. Artif. Intell..

[2]  Jean-Pierre Corriou,et al.  Model predictive control for wastewater treatment process with feedforward compensation , 2009 .

[3]  Lucas Barcelos de Oliveira,et al.  Multi-agent Model Predictive Control of Signaling Split in Urban Traffic Networks ∗ , 2010 .

[4]  Stephen J. Wright,et al.  Distributed MPC Strategies With Application to Power System Automatic Generation Control , 2008, IEEE Transactions on Control Systems Technology.

[5]  David J. Lovell,et al.  Autonomous Agents for Traffic Simulation and Control , 2001 .

[6]  William B. Dunbar,et al.  Distributed Receding Horizon Control of Dynamically Coupled Nonlinear Systems , 2007, IEEE Transactions on Automatic Control.

[7]  Nancy A. Lynch,et al.  Distributed Algorithms , 1992, Lecture Notes in Computer Science.

[8]  Eduardo Camponogara,et al.  Designing Communication Networks to Decompose Network Control Problems , 2005, INFORMS J. Comput..

[9]  Eduardo Camponogara,et al.  Distributed model predictive control , 2002 .

[10]  Lucas Barcelos de Oliveira,et al.  Distributed Optimization for Model Predictive Control of Linear-Dynamic Networks , 2009, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[11]  Naum Zuselevich Shor,et al.  Minimization Methods for Non-Differentiable Functions , 1985, Springer Series in Computational Mathematics.

[12]  Markos Papageorgiou,et al.  A Multivariable Regulator Approach to Traffic-Responsive Network-Wide Signal Control , 2000 .

[13]  Francesco Borrelli,et al.  Decentralized receding horizon control for large scale dynamically decoupled systems , 2009, Autom..

[14]  Eduardo Camponogara,et al.  Distributed Optimization for Model Predictive Control of Linear Dynamic Networks With Control-Input and Output Constraints , 2011, IEEE Transactions on Automation Science and Engineering.

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

[16]  Stephen J. Wright,et al.  Stability and optimality of distributed model predictive control , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[17]  Yan Zhang,et al.  Nash-optimization enhanced distributed model predictive control applied to the Shell benchmark problem , 2005, Inf. Sci..

[18]  William B. Dunbar,et al.  Distributed receding horizon control for multi-vehicle formation stabilization , 2006, Autom..