# Distributed ADMM for model predictive control and congestion control

@article{Mota2012DistributedAF, title={Distributed ADMM for model predictive control and congestion control}, author={Jo{\~a}o F. C. Mota and Jo{\~a}o M. F. Xavier and Pedro M. Q. Aguiar and Markus P{\"u}schel}, journal={2012 IEEE 51st IEEE Conference on Decision and Control (CDC)}, year={2012}, pages={5110-5115} }

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…

## 67 Citations

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## References

SHOWING 1-10 OF 20 REFERENCES

Distributed Optimization for Model Predictive Control of Linear Dynamic Networks With Control-Input and Output Constraints

- Computer Science, MathematicsIEEE Transactions on Automation Science and Engineering
- 2011

A distributed interior-point algorithm for solving DMPC optimization problems with a network of agents, one for each subsystem, which is shown to converge to an optimal solution in a traffic network.

Distributed model predictive control

- Mathematics, EngineeringProceedings of the 2001 American Control Conference. (Cat. No.01CH37148)
- 2001

A distributed model predictive control scheme that exchanges predictions by communication and incorporates the information from other controllers into their local MPC problem so as to coordinate with each other to show the performance of the scheme.

D-ADMM: A Communication-Efficient Distributed Algorithm for Separable Optimization

- Computer ScienceIEEE Transactions on Signal Processing
- 2013

D-ADMM is proven to converge when the network is bipartite or when all the functions are strongly convex, although in practice, convergence is observed even when these conditions are not met.

Understanding Vegas: a duality model

- Computer Science
- 2002

A multi-link multi-source model of the TCP Vegas congestion control mechanism is described, which implies that Vegas stabilizes around a weighted proportionally fair allocation of network capacity when there is sucien t buering in the network.

Understanding TCP Vegas: a duality model

- Computer Science
- 2002

A multilink multisource model of the TCP Vegas congestion control mechanism is described, which implies that Vegas stabilizes around a weighted proportionally fair allocation of network capacity when there is sufficient buffering in the network.

Distributed Optimization of Coupled Systems With Applications to Network Utility Maximization

- Computer Science2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings
- 2006

This work presents a systematic approach of consistency pricing to decouple NUM problems with coupled utilities, obtaining distributed algorithms that efficiently handle couplings in utilities with two alternative timescales, as well as a method to reduce message passing overhead in the case of interference-based coupling.

Stability and optimality of distributed model predictive control

- Mathematics, EngineeringProceedings of the 44th IEEE Conference on Decision and Control
- 2005

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.

Distributed model predictive control

- Mathematics
- 2002

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.

Layering as Optimization Decomposition: A Mathematical Theory of Network Architectures

- Computer ScienceProceedings of the IEEE
- 2007

A survey of the recent efforts towards a systematic understanding of layering as optimization decomposition, where the overall communication network is modeled by a generalized network utility maximization problem, each layer corresponds to a decomposed subproblem, and the interfaces among layers are quantified as functions of the optimization variables coordinating the subproblems.

Layering As Optimization Decomposition

- Computer Science
- 2006

This paper presents a survey of the recent efforts towards a systematic understanding of “layering” as “optimization decomposition”, where the overall communication network is modeled by a generalized Network Utility Maximization (NUM) problem, each layer corresponds to a decomposed subproblem, and the interfaces among layers are quantified as functions of the optimization variables coordinating the subproblems.