×

Co-design of \(H_\infty\) jump observers for event-based measurements over networks. (English) Zbl 1333.93184

Summary: This work presents a strategy to minimise the network usage and the energy consumption of wireless battery-powered sensors in the observer problem over networks. The sensor nodes implement a periodic send-on-delta approach, sending new measurements when a measure deviates considerably from the previous sent one. The estimator node implements a jump observer whose gains are computed offline and depend on the combination of available new measurements. We bound the estimator performance as a function of the sending policies and then state the design procedure of the observer under fixed sending thresholds as a semidefinite programming problem. We address this problem first in a deterministic way and, to reduce conservativeness, in a stochastic one after obtaining bounds on the probabilities of having new measurements and applying robust optimisation problem over the possible probabilities using sum of squares decomposition. We relate the network usage with the sending thresholds and propose an iterative procedure for the design of those thresholds, minimising the network usage while guaranteeing a prescribed estimation performance. Simulation results and experimental analysis show the validity of the proposal and the reduction of network resources that can be achieved with the stochastic approach.

MSC:

93C95 Application models in control theory
93A30 Mathematical modelling of systems (MSC2010)
93C55 Discrete-time control/observation systems
93C57 Sampled-data control/observation systems
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1016/j.automatica.2012.02.028 · Zbl 1401.93189 · doi:10.1016/j.automatica.2012.02.028
[2] DOI: 10.1016/j.jprocont.2012.09.005 · doi:10.1016/j.jprocont.2012.09.005
[3] DOI: 10.1016/j.conengprac.2014.06.002 · doi:10.1016/j.conengprac.2014.06.002
[4] DOI: 10.1109/TCST.2013.2279216 · doi:10.1109/TCST.2013.2279216
[5] DOI: 10.1109/TAC.2011.2164287 · Zbl 1368.93002 · doi:10.1109/TAC.2011.2164287
[6] DOI: 10.1109/TAC.2010.2046926 · Zbl 1368.93496 · doi:10.1109/TAC.2010.2046926
[7] Cormen T., Introduction to algorithms (2001) · Zbl 1047.68161
[8] DOI: 10.1109/TCST.2008.2010459 · doi:10.1109/TCST.2008.2010459
[9] DOI: 10.1080/00207721.2014.907944 · Zbl 1333.93234 · doi:10.1080/00207721.2014.907944
[10] DOI: 10.1002/rnc.3335 · Zbl 1333.93217 · doi:10.1002/rnc.3335
[11] DOI: 10.1109/TCST.2006.872504 · doi:10.1109/TCST.2006.872504
[12] DOI: 10.1049/iet-cta.2008.0542 · doi:10.1049/iet-cta.2008.0542
[13] DOI: 10.1109/TAC.2009.2017144 · Zbl 1367.90002 · doi:10.1109/TAC.2009.2017144
[14] DOI: 10.1016/j.automatica.2009.10.035 · Zbl 1213.93063 · doi:10.1016/j.automatica.2009.10.035
[15] DOI: 10.1080/00207721.2013.775387 · Zbl 1316.93108 · doi:10.1080/00207721.2013.775387
[16] DOI: 10.1109/TAC.2013.2294622 · Zbl 1360.93398 · doi:10.1109/TAC.2013.2294622
[17] DOI: 10.3390/S7102128 · doi:10.3390/S7102128
[18] DOI: 10.3390/s8020897 · doi:10.3390/s8020897
[19] DOI: 10.3390/s90403078 · doi:10.3390/s90403078
[20] DOI: 10.1002/rnc.2986 · Zbl 1302.93171 · doi:10.1002/rnc.2986
[21] DOI: 10.1109/CDC.2013.6760825 · doi:10.1109/CDC.2013.6760825
[22] DOI: 10.1109/TII.2010.2051812 · doi:10.1109/TII.2010.2051812
[23] DOI: 10.1109/TFUZZ.2010.2052259 · doi:10.1109/TFUZZ.2010.2052259
[24] DOI: 10.1109/TFUZZ.2012.2191790 · doi:10.1109/TFUZZ.2012.2191790
[25] DOI: 10.1109/TFUZZ.2009.2017378 · doi:10.1109/TFUZZ.2009.2017378
[26] DOI: 10.1016/j.jfranklin.2014.10.022 · Zbl 1307.93444 · doi:10.1016/j.jfranklin.2014.10.022
[27] DOI: 10.1016/j.conengprac.2014.08.004 · doi:10.1016/j.conengprac.2014.08.004
[28] DOI: 10.1109/TAC.2003.820140 · Zbl 1364.93785 · doi:10.1109/TAC.2003.820140
[29] DOI: 10.1109/MWC.2002.1028878 · doi:10.1109/MWC.2002.1028878
[30] DOI: 10.1016/j.automatica.2006.08.022 · Zbl 1111.93080 · doi:10.1016/j.automatica.2006.08.022
[31] DOI: 10.1109/TAC.2009.2012973 · Zbl 1367.93354 · doi:10.1109/TAC.2009.2012973
[32] DOI: 10.1109/TAC.2012.2215253 · Zbl 1369.90086 · doi:10.1109/TAC.2012.2215253
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.