Distributed scheduling of sensor networks for identification of spatio-temporal processes

Patan, Maciej

doi:10.2478/v10006-012-0022-9

Abstract

An approach to determine a scheduling policy for a sensor network monitoring some spatial domain in order to identify unknown parameters of a distributed system is discussed. Given a finite number of possible sites at which sensors are located, the activation schedule for scanning sensors is provided so as to maximize a criterion defined on the Fisher information matrix associated with the estimated parameters. The related combinatorial problem is relaxed through operating on the density of sensors in lieu of individual sensor positions. Then, based on the adaptation of pairwise communication algorithms and the idea of running consensus, a numerical scheme is developed which distributes the computational burden between the network nodes. As a result, a simple exchange algorithm is outlined to solve the design problem in a decentralized fashion.

References

Amouroux, M. and Babary, J. P. (1988). Sensor and control location problems, in M. G. Singh (Ed.), Systems & Control Encyclopedia. Theory, Technology, Applications, Vol. 6, Pergamon Press, Oxford, pp. 4238-4245.
Search in Google Scholar
Atkinson, A. C., Donev, A. N. and Tobias, R. (2007). Optimum Experimental Design, with SAS, Oxford University Press, Oxford.
Search in Google Scholar
Boyd, S., Ghosh, A., Prabhakar, B. and Shah, D. (2006). Randomized gossip algorithms, IEEE Transactions on Information Theory 52(6): 2508-2530.10.1109/TIT.2006.874516
Search in Google Scholar
Braca, P., Marano, S. and Matta, V. (2008). Enforcing consensus while monitoring the environment in wireless sensor network, IEEE Transactions on Signal Processing 56(7): 3375-3380.10.1109/TSP.2008.917855
Search in Google Scholar
Cassandras, C. G. and Li, W. (2005). Sensor networks and cooperative control, European Journal of Control 11(4-5): 436-463.10.3166/ejc.11.436-463
Search in Google Scholar
COMSOL AB (2007). COMSOLMultiphysics Modelling Guide, ver. 3.4.
Search in Google Scholar
Demetriou, M. A. (2000). Activation policy of smart controllers for flexible structures with multiple actuator/sensor pairs, Proceedings of the 14th International Symposium on Mathematical Theory of Networks and Systems, Perpignan, France, (on CD-ROM).
Search in Google Scholar
Demetriou, M. A. and Hussein, I. I. (2009). Estimation of spatially distributed processes using mobile spatially distributed sensor network, SIAM Journal on Control and Optimization 48(1): 266-291.10.1137/060677884
Search in Google Scholar
Fedorov, V. V. and Hackl, P. (1997). Model-Oriented Design of Experiments, Lecture Notes in Statistics, Vol. 125, Springer-Verlag, New York, NY.
Search in Google Scholar
Jeremić, A. and Nehorai, A. (2000). Landmine detection and localization using chemical sensor array processing, IEEE Transactions on Signal Processing 48(5): 1295-1305.10.1109/78.839977
Search in Google Scholar
Joshi, S. and Boyd, S. (2009). Sensor selection via convex optimization, IEEE Transactions on Signal Processing 57(2): 451-462.10.1109/TSP.2008.2007095
Search in Google Scholar
Kempe, D., Dobra, A. and Gehrke, J. (2003). Gossip-based computation of aggregate information, Proceedings of the Conference on Foundations of Computer Science, Cambridge, MA, USA, pp. 482-491.
Search in Google Scholar
Kubrusly, C. S. and Malebranche, H. (1985). Sensors and controllers location in distributed systems—A survey, Automatica 21(2): 117-128.10.1016/0005-1098(85)90107-4
Search in Google Scholar
Martínez, S. and Bullo, F. (2006). Optimal sensor placement and motion coordination for target tracking, Automatica 42(4): 661-668.10.1016/j.automatica.2005.12.018
Search in Google Scholar
Müller, W. G. (2007). Collecting Spatial Data: Optimum Design of Experiments for Random Fields, 3rd Edn., Physica-Verlag, Heidelberg.
Search in Google Scholar
Nehorai, A., Porat, B. and Paldi, E. (1995). Detection and localization of vapor-emitting sources, IEEE Transactions on Signal Processing 43(1): 243-253.10.1109/78.365304
Search in Google Scholar
Ögren, P., Fiorelli, E. and Leonard, N. E. (2004). Cooperative control of mobile sensor networks: Adaptive gradient climbing in a distributed environment, IEEE Transactions on Automatic Control 49(8): 1292-1302.10.1109/TAC.2004.832203
Search in Google Scholar
Patan, M. (2004). Optimal Observation Strategies for Parameter Estimation of Distributed Systems, Zielona Góra University Press, Zielona Góra, available at http://www.zbc.zgora.pl. http://www.zbc.zgora.pl
Search in Google Scholar
Patan, M. (2006). Optimal activation policies for continous scanning observations in parameter estimation of distributed systems, International Journal of Systems Science 37(11): 763-775.10.1080/00207720600825560
Search in Google Scholar
Patan, M. (2008). A parallel sensor scheduling technique for fault detection in distributed parameter systems, in E. Luque, T. Margalef and D. Benítez (Eds.) Euro-Par 2008: Parallel Processing, Lecture Notes in Computer Science, Vol. 5168, Springer-Verlag, Berlin/Heidelberg, pp. 833-843.10.1007/978-3-540-85451-7_88
Search in Google Scholar
Patan, M. (2009a). Decentralized mobile sensor routing for parameter estimation of distributed systems, Proceedings of the 1st IFAC Workshop on Estimation and Control of Networked Systems, NecSys 2009, Venice, Italy, pp. 210-215.10.3182/20090924-3-IT-4005.00036
Search in Google Scholar
Patan, M. (2009b). Distributed configuration of sensor networks for parameter estimation in spatio-temporal systems, Proceedings of the European Control Conference, ECC'09, Budapest, Hungary, pp. 4871-4876.
Search in Google Scholar
Patan, M., Chen, Y. and Tricaud, C. (2008). Resource-constrained sensor routing for parameter estimation of distributed systems, Proceedings of the 17th IFAC World Congress, Seoul, South Korea, (on DVD-ROM).10.3182/20080706-5-KR-1001.01314
Search in Google Scholar
Patan, M. and Patan, K. (2005). Optimal observation strategies for model-based fault detection in distributed systems, International Journal of Control 78(18): 1497-1510.10.1080/00207170500366077
Search in Google Scholar
Patan, M. and Uciński, D. (2005). Optimal activation strategy of discrete scanning sensors for fault detection in distributed-parameter systems, Proceedings of the 16th IFAC World Congress, Prague, Czech Republic, (on CD-ROM).10.3182/20050703-6-CZ-1902.01837
Search in Google Scholar
Patan, M. and Uciński, D. (2008). Configuring a sensor network for fault detection in distributed parameter systems, International Journal of Applied Mathematics and Computer Science 18(4): 513-524, DOI: 10.2478/v10006-008-0045-4.10.2478/v10006-008-0045-4
Search in Google Scholar
Patan, M. and Uciński, D. (2010a). Sensor scheduling with selection of input experimental conditions for identification of distributed systems, Methods and Models in Automation and Robotics, MMAR 2010: 15th International Conference, Międzyzdroje, Poland, pp. 148-153.10.1109/MMAR.2010.5587245
Search in Google Scholar
Patan, M. and Uciński, D. (2010b). Time-constrained sensor scheduling for parameter estimation of distributed systems, Proceedings of the 49th IEEE Conference on Decision and Control, Atlanta, GA, USA, pp. 7-12.10.1109/CDC.2010.5717912
Search in Google Scholar
Point, N., Vande Wouwer, A. and Remy, M. (1996). Practical issues in distributed parameter estimation: Gradient computation and optimal experiment design, Control Engineering Practice 4(11): 1553-1562.10.1016/0967-0661(96)00169-4
Search in Google Scholar
Porat, B. and Nehorai, A. (1996). Localizing vapor-emitting sources by moving sensors, IEEE Transactions on Signal Processing 44(4): 1018-1021.10.1109/78.492560
Search in Google Scholar
Quereshi, Z. H., Ng, T. S. and Goodwin, G. C. (1980). Optimum experimental design for identification of distributed parameter systems, International Journal of Control 31(1): 21-29.10.1080/00207178008961025
Search in Google Scholar
Rafajłowicz, E. (1983). Optimal experiment design for identification of linear distributed-parameter systems: Frequency domain approach, IEEE Transactions on Automatic Control 28(7): 806-808.10.1109/TAC.1983.1103309
Search in Google Scholar
Rafajłowicz, E. (1986). Optimum choice of moving sensor trajectories for distributed parameter system identification, International Journal of Control 43(5): 1441-1451.10.1080/00207178608933550
Search in Google Scholar
Rao, M. M. (1987). Measure Theory and Integration, John Wiley & Sons, New York, NY.
Search in Google Scholar
Song, Z., Chen, Y., Sastry, C. and Tas, N. (2009). Optimal Observation for Cyber-physical Systems: A Fisher-Information-Matrix-Based Approach, Springer-Verlag, Berlin/Heidelberg.10.1007/978-1-84882-656-4
Search in Google Scholar
Sun, N.-Z. (1994). Inverse Problems in Groundwater Modeling, Theory and Applications of Transport in Porous Media, Kluwer Academic Publishers, Dordrecht.
Search in Google Scholar
Uciński, D. (2000a). Optimal selection of measurement locations for parameter estimation in distributed processes, International Journal of Applied Mathematics and Computer Science 10(2): 357-379.
Search in Google Scholar
Uciński, D. (2000b). Optimal sensor location for parameter estimation of distributed processes, International Journal of Control 73(13): 1235-1248.10.1080/002071700417876
Search in Google Scholar
Uciński, D. (2005). Optimal Measurement Methods for Distributed-Parameter System Identification, CRC Press, Boca Raton, FL.10.1201/9780203026786
Search in Google Scholar
Uciński, D. and Chen, Y. (2005). Time-optimal path planning of moving sensors for parameter estimation of distributed systems, Proceedings of the 44th IEEE Conference on Decision and Control/European Control Conference 2005, Seville, Spain, (on CD-ROM).
Search in Google Scholar
Uciński, D. and Demetriou, M. A. (2004). An approach to the optimal scanning measurement problem using optimum experimental design, Proceedings of the American Control Conference, Boston, MA, USA, (on CD-ROM).10.23919/ACC.2004.1386808
Search in Google Scholar
Uciński, D. and Patan, M. (2002). Optimal location of discrete scanning sensors for parameter estimation of distributed systems, Proceedings of the 15th IFAC World Congress, Barcelona, Spain, (on CD-ROM).10.3182/20020721-6-ES-1901.00459
Search in Google Scholar
Uciński, D. and Patan, M. (2007). D-optimal design of a monitoring network for parameter estimation of distributed systems, Journal of Global Optimization 39(2): 291-322.10.1007/s10898-007-9139-z
Search in Google Scholar
Uciński, D. and Patan, M. (2010). Sensor network design for the estimation on spatially distributed processes, International Journal of Applied Mathematics and Computer Science 20(3): 459-481, DOI: 10.2478/v10006-010-0034-2.10.2478/v10006-010-0034-2
Search in Google Scholar
van de Wal, M. and de Jager, B. (2001). A review of methods for input/output selection, Automatica 37(4): 487-510.10.1016/S0005-1098(00)00181-3
Search in Google Scholar
Xiao, L. and Boyd, S. (2004). Fast linear iterations for distributed averaging, Systems and Control Letters 53(1): 65-78.10.1016/j.sysconle.2004.02.022
Search in Google Scholar

Distributed scheduling of sensor networks for identification of spatio-temporal processes

Abstract

Paradigm

My account