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

Patan, M.

International Journal of Applied Mathematics and Computer Science, Tome 22 (2012) no. 2, pp. 299-311.

Résumé

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.

Détail

Keywords: distributed parameter system, parameter estimation, running consensus, scanning measurements
Mots-clés : układ o parametrach rozłożonych, estymacja parametrów, pomiar skaningowy, sieć sensorowa

Bibliographie

[1] 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.

[2] Atkinson, A. C., Donev, A. N. and Tobias, R. (2007). Optimum Experimental Design, with SAS, Oxford University Press, Oxford.

[3] Boyd, S., Ghosh, A., Prabhakar, B. and Shah, D. (2006). Randomized gossip algorithms, IEEE Transactions on Information Theory 52(6): 2508-2530.

[4] 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.

[5] Cassandras, C. G. and Li, W. (2005). Sensor networks and cooperative control, European Journal of Control 11(4-5): 436-463.

[6] COMSOL AB (2007). COMSOLMultiphysics Modelling Guide, ver. 3.4.

[7] 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).

[8] 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.

[9] Fedorov, V. V. and Hackl, P. (1997). Model-Oriented Design of Experiments, Lecture Notes in Statistics, Vol. 125, Springer-Verlag, New York, NY.

[10] Jeremić, A. and Nehorai, A. (2000). Landmine detection and localization using chemical sensor array processing, IEEE Transactions on Signal Processing 48(5): 1295-1305.

[11] Joshi, S. and Boyd, S. (2009). Sensor selection via convex optimization, IEEE Transactions on Signal Processing 57(2): 451-462.

[12] 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.

[13] Kubrusly, C. S. and Malebranche, H. (1985). Sensors and controllers location in distributed systems-A survey, Automatica 21(2): 117-128.

[14] Martínez, S. and Bullo, F. (2006). Optimal sensor placement and motion coordination for target tracking, Automatica 42(4): 661-668.

[15] Müller, W. G. (2007). Collecting Spatial Data: Optimum Design of Experiments for Random Fields, 3rd Edn., Physica-Verlag, Heidelberg.

[16] Nehorai, A., Porat, B. and Paldi, E. (1995). Detection and localization of vapor-emitting sources, IEEE Transactions on Signal Processing 43(1): 243-253.

[17] 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.

[18] 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.

[19] 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.

[20] 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.

[21] 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.

[22] 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.

[23] 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).

[24] 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.

[25] 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).

[26] 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.

[27] 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.

[28] 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.

[29] 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.

[30] Porat, B. and Nehorai, A. (1996). Localizing vapor-emitting sources by moving sensors, IEEE Transactions on Signal Processing 44(4): 1018-1021.

[31] 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.

[32] 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.

[33] Rafajłowicz, E. (1986). Optimum choice of moving sensor trajectories for distributed parameter system identification, International Journal of Control 43(5): 1441-1451.

[34] Rao, M. M. (1987). Measure Theory and Integration, John Wiley Sons, New York, NY.

[35] 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.

[36] Sun, N.-Z. (1994). Inverse Problems in Groundwater Modeling, Theory and Applications of Transport in Porous Media, Kluwer Academic Publishers, Dordrecht.

[37] 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.

[38] Uciński, D. (2000b). Optimal sensor location for parameter estimation of distributed processes, International Journal of Control 73(13): 1235-1248.

[39] Uciński, D. (2005). Optimal Measurement Methods for Distributed-Parameter System Identification, CRC Press, Boca Raton, FL.

[40] 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).

[41] 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).

[42] 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).

[43] 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.

[44] 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.

[45] van de Wal, M. and de Jager, B. (2001). A review of methods for input/output selection, Automatica 37(4): 487-510.

[46] Xiao, L. and Boyd, S. (2004). Fast linear iterations for distributed averaging, Systems and Control Letters 53(1): 65-78.