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Distributed Predictive Control Using Population Games

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The Role of Population Games in the Design of Optimization-Based Controllers

Part of the book series: Springer Theses ((Springer Theses))

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Abstract

In Chap. 3, the role of the population games in the dynamical tuning for MPC controllers has been presented. This chapter presents a different role of population games consisting in the design of DMPC controllers involving resource allocation problems.

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Notes

  1. 1.

    A graph is considered to be well connected if the connectivity of the graph does not depend on few nodes, e.g., a path graph is not well connected since the removal of any node involving two edges would disconnect the graph (connectivity relies on \(n-2\) nodes), whereas a complete graph is considered well connected since the removal of a node does not imply the disconnection of the graph (connectivity does not depend on any node).

  2. 2.

    In the consensus problem, it is desired to achieve the agreement among different variables, e.g., \(p^\star _i=p^\star _j\), for all \(i,j \in \{1,\ldots ,n\}\), objective that can be achieved taking advantage of the convergence result when \(\mathbf{p}^{\star }\in \mathrm {int}\Delta \), i.e., \(f_i(\mathbf{p}^\star )=f_j(\mathbf{p}^\star )\) under the population-game framework.

  3. 3.

    DSD have been selected to illustrate the methodology. However, any of the distributed population dynamics can be used.

  4. 4.

    Notice that \(\mathbf{E}_{i,k}\) is a constant known value at each iteration since \(\varvec{\Phi }_i\) and \(\varvec{\Psi }_i\) are constant and the current system state \(\mathbf{x}_{i,k|k}\) is also known for all \(i = 1,\ldots , m\). Therefore, \(\mathbf{G}_{i,k}\) is also constant at each iteration.

References

  1. Barreiro-Gomez J, Obando G, Quijano N (2017) Distributed population dynamics: optimization and control applications. IEEE Trans Syst Man Cybern: Syst 47(2):304–314

    Google Scholar 

  2. Barreiro-Gomez J, Obando G, Ocampo-Martinez C, Quijano N (2015) Making non-centralized a model predictive control scheme by using distributed smith dynamics. In: Proceedings of the 5th IFAC conference on nonlinear model predictive control. Seville, Spain, pp 501–506

    Google Scholar 

  3. Sandholm WH (2010) Population games and evolutionary dynamics Mass. MIT Press, Cambridge

    MATH  Google Scholar 

  4. Pantoja A, Quijano N (2012) Distributed optimization using population dynamics with a local replicator equation. In: Proceedings of the 51st IEEE conference on decision and control (CDC). Maui, Hawaii, pp 3790–3795

    Google Scholar 

  5. Moreau L (2005) Stability of multiagent systems with time-dependent communication links. IEEE Trans Autom Control 50(2):169–182

    Article  MathSciNet  Google Scholar 

  6. Olfati-Saber R, Fax JA, Murray RM (2007) Consensus and cooperation in networked multi-agent systems. Proc IEEE 95(1):215–233

    Article  Google Scholar 

  7. Ren W, Beard RW (2005) Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Trans Autom Control 50(5):655–661

    Article  MathSciNet  Google Scholar 

  8. Bornholdt S, Schuster HG (2003) Handbook of graphs and networks, 2nd edn. Wiley Online Library,

    MATH  Google Scholar 

  9. Maestre JM, Negenborn RR (2013) Distributed model predictive control made easy, vol 69. Springer Science and Business Media, Berlin

    Google Scholar 

  10. Boyd S, Parikh N, Chu E, Peleato B, Eckstein J (2011) Distributed optimization and statistical learning via the alternating direction method of multipliers. Found Trends Mach Learn 3(1):1–122

    Article  Google Scholar 

  11. Mota J, Xavier J, Aguiar P, Puschel M (2013) D-ADMM: a communication-efficient distributed algorithm for separable optimization. IEEE Trans Signal Process 61(10):2718–2723

    Article  MathSciNet  Google Scholar 

  12. Costa RP, Lemos JM, Mota JFC, Xavier JMF (2014) D-ADMM based distributed MPC with input–output models. In: Proceedings of the 53rd IEEE conference on control applications (CCA). Antibes-Juan Les Pins, France, pp 699–704

    Google Scholar 

  13. Stewart BT, Venkat AN, Rawlings JB, Wright SJ, Pannocchia G (2010) Cooperative distributed model predictive control. Syst Control Lett 59(8):460–469

    Article  MathSciNet  Google Scholar 

  14. Ferramosca A, Limon D, Alvarado I, Camacho EF (2013) Cooperative distributed MPC for tracking. Automatica 49(2013):906–914

    Article  MathSciNet  Google Scholar 

  15. Trodden P, Richards A (2013) Cooperative distributed MPC of linear systems with coupled constraints. Automatica 49(2):479–487

    Article  MathSciNet  Google Scholar 

  16. Riverso S, Farina M, Ferrari-Trecate G (2013) Plug-and-play decentralized model predictive control for linear systems. IEEE Trans Autom Control 58(10):2608–2614

    Article  MathSciNet  Google Scholar 

  17. Riverso S, Farina M, Ferrari-Trecate G (2014) Plug-and-play model predictive control based on robust control invariant sets. Automatica 50(2014):2179–2186

    Article  MathSciNet  Google Scholar 

  18. Zeilinger MN, Y-Pu, Riverso S, Ferrari-Trecate G, Jones CN (2013) Plug and play distributed model predictive control based on distributed invariance and optimization. In: Proceedings of the 52nd IEEE conference on decision and control (CDC). Florenze, Italy, pp 5770–5776

    Google Scholar 

  19. Hu B, Linnemann A (2002) Towards infinite-horizon optimality in nonlinear model predictive control. IEEE Trans Autom Control 47(4):679–682

    Article  MathSciNet  Google Scholar 

  20. Limon D, Alamo T, Camacho EF (2005) Enlarging the domain of attraction of MPC controllers. Automatica 41(2005):629–635

    Article  MathSciNet  Google Scholar 

  21. Rawlings JB, Mayne DQ (2009) Model predictive control: theory and design. Nob Hill Publishing. ISBN 9780975937709

    Google Scholar 

  22. Rawlings JB, Bonné D, Jørgensen JB, Venkat AN, Jørgensen SB (2008) Unreachable setpoints in model predictive control. IEEE Trans Autom Control 53(9):2209–2215

    Article  MathSciNet  Google Scholar 

  23. Domínguez-García AD, Hadjicostis CN (2011) Distributed algorithms for control of demand response and distributed energy resources. In: Proceedings of the 50th IEEE conference on decision and control and European control conference, (CDC-ECC). Orlando, Florida, pp 27–32

    Google Scholar 

  24. Garin F, Schenato L (2010) A survey on distributed estimation and control applications using linear consensus algorithms. Netw Control Syst 406:75–107

    Article  MathSciNet  Google Scholar 

  25. Maciejowski J (2002) Predictive control: with constraints. Pearson Education, New York

    MATH  Google Scholar 

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Authors and Affiliations

  1. Learning and Game Theory Laboratory, Engineering Division, New York University, Abu Dhabi, United Arab Emirates

    Julian Barreiro-Gomez

  2. Department of Automatic Control, Institut de Robòtica i Informàtica Industrial (CSIC-UPC), Universitat Politècnica de Catalunya, Barcelona, Spain

    Julian Barreiro-Gomez

  3. Departamento de Ingeniería Eléctrica y Electrónica, Universidad de los Andes, Bogotá, Colombia

    Julian Barreiro-Gomez

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  1. Julian Barreiro-Gomez
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Correspondence to Julian Barreiro-Gomez .

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Barreiro-Gomez, J. (2019). Distributed Predictive Control Using Population Games. In: The Role of Population Games in the Design of Optimization-Based Controllers. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-92204-1_4

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