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Distributed control of linear systems allowing choices. (English) Zbl 1353.93008

Summary: Distributed choice-based control systems are systems for which the applied control of each agent is individually selected according to the agent’s choice. They form an interesting class of decentralized systems in which control strategies are entangled with the information structure. This paper focuses on an important subset of these systems that are governed by linear dynamics. We show how choice-based targets can be realized without explicit communication and how control actions can serve as signaling tools. In comparison with strategies using explicit communication methods, the value of information in facilitating cost reduction is revealed. Our solution approach makes use of a composite cost function that incorporates both control costs and target errors for benchmarking.

MSC:

93A14 Decentralized systems
93C05 Linear systems in control theory
49N05 Linear optimal control problems
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[1] J. Baillieul and P. J. Antsaklis, {\it Control and communication challenges in networked real-time systems}, Proc. IEEE, 95 (2007), pp. 9-28.
[2] J. Baillieul and K. Ozcimder, {\it The control theory of motion-based communication: Problems in teaching robots to dance}, in Proceedings of the American Control Conference, Montreal, Canada, 2012, pp. 4319-4326.
[3] R. Bansal and T. Başar, {\it Stochastic teams with nonclassical information revisited: When is an affine law optimal?}, IEEE Trans. Automat. Control, 32 (1987), pp. 554-559. · Zbl 0633.93061
[4] A. E. Bryson and Y.-C. Ho, {\it Applied Optimal Control: Optimization, Estimation, and Control}, Taylor & Francis, New York, 1975.
[5] J. Corfmat and A. S. Morse, {\it Decentralized control of linear multivariable systems}, Automatica J. IFAC, 12 (1976), pp. 479-495. · Zbl 0347.93019
[6] P. Grover, {\it Actions can speak more clearly than words}, Ph.D. thesis, EECS Department, University of California, Berkeley, CA, 2011.
[7] P. Grover, S. Y. Park, and A. Sahai, {\it Approximately optimal solutions to the finite-dimensional Witsenhausen counterexample}, IEEE Trans. Automat. Control, 58 (2013), pp. 2189-2204. · Zbl 1369.93719
[8] G. Guo, Z. Liu, and W. S. Wong, {\it Coordinated optimal target realization for linear systems allowing choice-based actions}, Optimal Control Appl. Methods, submitted. · Zbl 1348.93008
[9] J. P. Hespanha, P. Naghshtabrizi, and Y. Xu, {\it A survey of recent results in networked control systems}, Proc. IEEE, 95 (2007), pp. 138-162.
[10] Y.-C. Ho, {\it Team decision theory and information structures}, Proc. IEEE, 68 (1980), pp. 644-654.
[11] A. Jones and S. Andersson, {\it A motion-based communication system}, in Proceedings of the American Control Conference, Washington, DC, 2013, pp. 365-370.
[12] V. Kapila and A. G. Sparks, {\it Spacecraft formation flying: Dynamics and control}, J. Guidance Control Dynam., 23 (2000), pp. 561-564.
[13] E. Kushilevitz and N. Nisan, {\it Communication Complexity}, Cambridge University Press, New York, 1997. · Zbl 0869.68048
[14] Z. Liu and W. S. Wong, {\it Choice-based cluster consensus in multi-agent systems}, in Proceedings of the Chinese Control Conference, Xi’an, China, 2013, pp. 7285-7290.
[15] Z. Liu and W. S. Wong, {\it Control and signaling in distributed linear control systems allowing choices}, in Proceedings of the American Control Conference, Portland, OR, 2014, pp. 5724-5729.
[16] Z. Liu, W. S. Wong, and G. Guo, {\it Cooperative control of linear systems with choice actions}, in Proceedings of the American Control Conference, Washington, DC, 2013, pp. 5394-5399.
[17] A. Mahajan, {\it Optimal decentralized control of coupled subsystems with control sharing}, IEEE Trans. Automat. Control, 58 (2013), pp. 2377-2382. · Zbl 1369.93721
[18] M. S. Mahmoud, {\it Decentralized Control and Filtering in Interconnected Dynamic Systems}, CRC Press, New York, 2011. · Zbl 1226.93004
[19] R. Mirghaderi, S. Adlakha, S. Lall, and A. Goldsmith, {\it Hat guessing games and the use of coding for decentralized control}, in Proceedings of the 49th IEEE Conference on Decision and Control, Atlanta, GA, 2010, pp. 979-985.
[20] S. Mitter and A. Sahai, {\it Information and control: Witsenhausen revisited}, in Learning, Control and Hybrid Systems, Lecture Notes in Control and Inform. Sci. 241, Y. Yamamoto and S. Hara, eds., Springer, New York, 1999, pp. 281-293. · Zbl 0945.93027
[21] R. Olfati-Saber, {\it Flocking for multi-agent dynamic systems: Algorithms and theory}, IEEE Trans. Automat. Control, 51 (2006), pp. 401-420. · Zbl 1366.93391
[22] D. V. Raghunathan and J. Baillieul, {\it Exploiting information content in relative motion}, in Proceedings of the American Control Conference, St. Louis, MO, 2009, pp. 2166-2171.
[23] N. Sandell, Jr., P. Varaiya, M. Athans, and M. Safonov, {\it Survey of decentralized control methods for large scale systems}, IEEE Trans. Automat. Control, 23 (1978), pp. 108-128. · Zbl 0385.93001
[24] H. S. Witsenhausen, {\it A counterexample in stochastic optimum control}, SIAM J. Control, 6 (1968), pp. 131-147. · Zbl 0159.13404
[25] W. S. Wong, {\it Control communication complexity of distributed control systems}, SIAM J. Control Optim., 48 (2009), pp. 1722-1742. · Zbl 1282.93028
[26] W. S. Wong and J. Baillieul, {\it Control communication complexity of nonlinear systems}, Commun. Inf. Syst., 9 (2009), pp. 103-140. · Zbl 1194.93015
[27] W. S. Wong and J. Baillieul, {\it Control communication complexity of distributed actions}, IEEE Trans. Automat. Control, 57 (2012), pp. 2731-2745. · Zbl 1369.93201
[28] S. Yüksel and T. Başar, {\it Optimal signaling policies for decentralized multicontroller stabilizability over communication channels}, IEEE Trans. Automat. Control, 52 (2007), pp. 1969-1974. · Zbl 1366.93029
[29] S. Yüksel and T. Başar, {\it Stochastic Networked Control Systems}, Springer, New York, 2013. · Zbl 1280.93003
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