# A Finite-Time Dual Method for Negotiation between Dynamical Systems

@article{Zelazo2013AFD, title={A Finite-Time Dual Method for Negotiation between Dynamical Systems}, author={Daniel Zelazo and Mathias B{\"u}rger and Frank Allg{\"o}wer}, journal={SIAM J. Control. Optim.}, year={2013}, volume={51}, pages={172-194} }

This work presents a distributed algorithm for online negotiations of an optimal control policy between dynamical systems. We consider a network of self-interested agents that must agree upon a common state within a specified finite time. The proposed algorithm exploits the distributed structure of the corresponding dual problem and uses a “shrinking horizon” property to enforce the finite-time constraint. It is shown that this algorithm evolves like a time-varying and linear dynamical system…

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## References

SHOWING 1-10 OF 29 REFERENCES

### A Distributed Real-Time Algorithm for Preference-Based Agreement

- Computer Science
- 2011

The algorithm is shown to be equivalent to a linear time-varying dynamical system with a distributed structure, and the error between the multiplier values of the algorithm and the corresponding centralized solution is given as an LTV system.

### Consensus and Cooperation in Networked Multi-Agent Systems

- Computer ScienceProceedings of the IEEE
- 2007

This paper provides a theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in…

### Distributed Subgradient Methods for Multi-Agent Optimization

- Mathematics, Computer ScienceIEEE Transactions on Automatic Control
- 2009

The authors' convergence rate results explicitly characterize the tradeoff between a desired accuracy of the generated approximate optimal solutions and the number of iterations needed to achieve the accuracy.

### On Distributed Convex Optimization Under Inequality and Equality Constraints

- Computer Science, MathematicsIEEE Transactions on Automatic Control
- 2012

Two distributed primal-dual subgradient algorithms can be implemented over networks with dynamically changing topologies but satisfying a standard connectivity property, and allow the agents to asymptotically agree on optimal solutions and optimal values of the optimization problem under the Slater's condition.

### A Randomized Incremental Subgradient Method for Distributed Optimization in Networked Systems

- Computer ScienceSIAM J. Optim.
- 2009

An algorithm that generalizes the randomized incremental subgradient method with fixed stepsize due to Nedic and Bertsekas is presented, particularly suitable for distributed implementation and execution, and possible applications include distributed optimization, e.g., parameter estimation in networks of tiny wireless sensors.

### A survey of consensus problems in multi-agent coordination

- MathematicsProceedings of the 2005, American Control Conference, 2005.
- 2005

As a distributed solution to multi-agent coordination, consensus or agreement problems have been studied extensively in the literature. This paper provides a survey of consensus problems in…

### Preference Based Group Agreement in Cooperative Control

- Computer Science
- 2010

Two different fully distributed coordination algorithms are proposed and analyzed, where different agents are modeled as double integrator systems and each agent aims to minimize a convex optimization function on the velocity.

### Problems in decentralized decision making and computation

- Computer Science
- 1984

A scheme whereby a set of decision makers (processors) exchange and update tentative decisions which minimize a common cost function, given information they possess is considered; it is shown that they are guaranteed to converge to consensus.

### Edge Agreement: Graph-Theoretic Performance Bounds and Passivity Analysis

- MathematicsIEEE Transactions on Automatic Control
- 2011

The dynamics induced by the edge Laplacian facilitates a better understanding of the role of certain subgraphs in the original agreement problem, and is employed to provide new insights into the nonlinear extension of linear agreement to agents with passive dynamics.