×

Optimal multiplexing of sparse controllers for linear systems. (English) Zbl 1429.93149

Summary: This article treats two problems of sparse and optimal multiplexing a finite ensemble of linear control systems. Given an ensemble of linear control systems, multiplexing of the controllers consists of an algorithm that selects, at each time \(t\), only one from the ensemble of linear systems is actively controlled whereas the other systems evolve in open-loop. The first problem treated here is a ballistic reachability problem where the control signals are required to be maximally sparse and multiplexed and the second concerns sparse and optimally multiplexed linear quadratic control. Numerical experiments are provided to demonstrate the efficacy of the techniques developed here.

MSC:

93C05 Linear systems in control theory
93B03 Attainable sets, reachability
49N10 Linear-quadratic optimal control problems
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Branicky, M. S.; Phillips, S. M.; Zhang, W., Scheduling and feedback co-design for networked control systems, (Proceedings of the 41st IEEE conference on decision and control, 2002., Vol. 2 (2002)), 1211-1217
[2] Chatterjee, D.; Nagahara, M.; Quevedo, D. E.; Rao, K. S.M., Characterization of maximum hands-off control, Systems & Control Letters, 94, 31-36 (2016) · Zbl 1344.93047
[3] Chowdhury, S.; Jing, W.; Cappelleri, D. J., Controlling multiple microrobots: recent progress and future challenges, Journal of Micro-Bio Robotics, 10, 1-11 (2015)
[4] Clarke, F. H., (Functional analysis, calculus of variations and optimal control. Functional analysis, calculus of variations and optimal control, Graduate texts in mathematics, vol. 264 (2013), Springer: Springer London)
[5] DiBenedetto, E., (Real analysis. Real analysis, Birkhäuser advanced texts (2002), Birkhäuser: Birkhäuser Boston)
[7] Farias, C.; Pirmez, L.; Delicato, F.; Carmo, L.; Li, W.; Zomaya, A. Y., Multisensor data fusion in shared sensor and actuator networks, (17th international conference on information fusion (FUSION) (2014)), 1-8
[8] de Farias, C. M.; Pirmez, L.; Delicato, F. C.; Li, W.; Zomaya, A. Y.; de Souza, J. N., A scheduling algorithm for shared sensor and actuator networks, (The international conference on information networking 2013 (ICOIN) (2013)), 648-653
[9] Filippov, A. F., (Differential equations with discontinuous righthand sides. Differential equations with discontinuous righthand sides, Mathematics and its applications (soviet series), vol. 18 (1988), Kluwer Academic Publishers Group: Kluwer Academic Publishers Group Dordrecht), Translated from the Russian
[10] Fleming, W. H.; Rishel, R. W., (Deterministic and stochastic optimal control. Deterministic and stochastic optimal control, Applications of mathematics, vol. 1 (1975), Springer) · Zbl 0323.49001
[11] Jovanović, M.; Lin, F., Sparse quadratic regulator, (Proceedings of the european control conference (ECC) (2013)), 1047-1052
[12] der Maas, A. V.; Steinbuch, Y. F.; Boverhof, A.; Heemels, W. P.M. H., Switched control of a scara robot with shared actuation resources, IFAC-PapersOnLine, 50, 1931-1936 (2017), 20th IFAC World Congress
[13] Nagahara, M.; Matsuda, T.; Hayashi, K., Compressive sampling for remote control systems, EICE Transactions on Fundamentals, E95-A, 713-722 (2012)
[14] Nagahara, M.; Quevedo, D. E.; Nešić, D., Maximum hands-off control: a paradigm of control effort minimization, IEEE Transactions on Automatic Control, 61 (2016) · Zbl 1359.49005
[15] Polyak, B.; Khlebnikov, M.; Shcherbakov, P., Sparse feedback in linear control systems, Automation and Remote Control, 75, 2099-2111 (2014) · Zbl 1327.93196
[16] Ross, I. M., A primer on pontryagin’s principle in optimal control (2015), Collegiate Publishers
[17] Saha, I.; Baruah, S.; Majumdar, R., Dynamic scheduling for networked control systems, (Proceedings of the 18th international conference on hybrid systems: Computation and control. Proceedings of the 18th international conference on hybrid systems: Computation and control, HSCC ’15 (2015), ACM), 98-107 · Zbl 1364.68124
[18] Srikant, S.; Akella, M. R., Precision attitude stabilization: incorporating rise and fall times in gas-based thrusters, Journal of Guidance, Control and Dynamics, 34, 317-323 (2011)
[19] Srikant, S.; Chatterjee, D., A jammer’s perspective of reachability and LQ optimal control, Automatica, 70, 295-302 (2016) · Zbl 1339.93024
[20] Sun, Z.; Ge, S. S., Analysis and synthesis of switched linear control systems, Automatica Journal of IFAC, 41, 181-195 (2005) · Zbl 1074.93025
[21] Zhang, L.; Hristu-Varsakelis, D., Communication and control co-design for networked control systems, Automatica, 42, 953-958 (2006) · Zbl 1117.93302
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.