Distributed ADMM for model predictive control and congestion control

Many problems in control can be modeled as an optimization problem over a network of nodes. Solving them with distributed algorithms provides advantages over centralized solutions, such as privacy and the ability to process data locally. In this paper, we solve optimization problems in networks where each node requires only partial knowledge of the problem's solution. We explore this feature to design a decentralized algorithm that allows a significant reduction in the total number of communications. Our algorithm is based on the Alternating Direction of Multipliers (ADMM), and we apply it to distributed Model Predictive Control (MPC) and TCP/IP congestion control. Simulation results show that the proposed algorithm requires less communications than previous work for the same solution accuracy.

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

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

[3]  S. Low,et al.  Understanding Vegas: a duality model , 2002 .

[4]  Georgios B. Giannakis,et al.  Distributed In-Network Channel Decoding , 2009, IEEE Transactions on Signal Processing.

[5]  Daniel Pérez Palomar,et al.  A tutorial on decomposition methods for network utility maximization , 2006, IEEE Journal on Selected Areas in Communications.

[6]  Yurii Nesterov,et al.  Introductory Lectures on Convex Optimization - A Basic Course , 2014, Applied Optimization.

[7]  Stephen P. Boyd,et al.  Fast Model Predictive Control Using Online Optimization , 2010, IEEE Transactions on Control Systems Technology.

[8]  Daniel Pérez Palomar,et al.  Distributed Optimization of Coupled Systems With Applications to Network Utility Maximization , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.

[9]  Alberto Bemporad,et al.  Synthesis of networked switching linear decentralized controllers , 2010, 49th IEEE Conference on Decision and Control (CDC).

[10]  João M. F. Xavier,et al.  D-ADMM: A Communication-Efficient Distributed Algorithm for Separable Optimization , 2012, IEEE Transactions on Signal Processing.

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

[12]  Steven H. Low,et al.  Understanding TCP Vegas: a duality model , 2002 .

[13]  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.

[14]  A. Robert Calderbank,et al.  Layering As Optimization Decomposition , 2006 .

[15]  A. Robert Calderbank,et al.  Layering as Optimization Decomposition: A Mathematical Theory of Network Architectures , 2007, Proceedings of the IEEE.

[16]  Bruce H. Krogh,et al.  Distributed model predictive control , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).