# zbMATH — the first resource for mathematics

Finite-horizon filtering for a class of nonlinear time-delayed systems with an energy harvesting sensor. (English) Zbl 1411.93176
Summary: In this paper, the finite-horizon filtering problem is investigated for a class of nonlinear time-delayed systems with an energy harvesting sensor. We consider a situation where the filter is located in a remote area from the sensor and the transmission of the measurements from the sensor to the filter may consume certain energy stored in sensor. The underlying sensor is capable of harvesting the energy from the environment. The transmission of the measurements is closely related to the sensor’s energy level and, for the remote filter, the measurements are regarded as missing when the sensor energy is insufficient to maintain the normal communication between the sensor and the filter. In order to derive the missing rate of the measurements, the probability distribution of the amount of the sensor energy is calculated recursively at each time instant. Then, in the presence of parameter nonlinearities, time delays as well as the probabilistic missing measurements resulting from the limited capacity of the sensor, we design a finite-horizon filter such that an upper bound is guaranteed on the filtering error covariance at each time instant and the filter gain minimizing such an upper bound is subsequently obtained in terms of the solution to a set of recursive equations. Finally, a numerical simulation example is employed to demonstrate the effectiveness of the proposed filtering scheme.

##### MSC:
 93E11 Filtering in stochastic control theory 93E10 Estimation and detection in stochastic control theory 93C10 Nonlinear systems in control theory
Full Text:
##### References:
 [1] Basin, M.; Hernandez-Gonzalez, M., Discrete-time $$H_\infty$$ filtering for nonlinear polynomial systems, International Journal of Systems Science, 47, 9, 2058-2066, (2016) · Zbl 1345.93153 [2] Basin, M.; Rodriguez-Gonzalez, J.; Martinez-Zuniga, R., Optimal filtering for linear state delay systems, IEEE Transactions on Automatic Control, 50, 5, 684-690, (2005) · Zbl 1365.93496 [3] Caballero-Aguila, R.; Hermoso-Carazo, A.; Linares-Perez, J., Distributed fusion filters from uncertain measured outputs in sensor networks with random packet losses, Information Fusion, 34, 70-79, (2017) · Zbl 1371.93184 [4] Chen, X.; Lam, J.; Li, P., Positive filtering for continuous-time positive systems under $$L_1$$ performance, International Journal of Control, 87, 9, 1906-1913, (2014) · Zbl 1317.93248 [5] de Saporta, B.; Costa, E. F., Approximate Kalman-Bucy filter for continuous-time semi-Markov jump linear systems, IEEE Transactions on Automatic Control, 61, 8, 2035-2048, (2016) · Zbl 1359.93500 [6] Devillers, B.; Gunduz, D., A general framework for the optimization of energy harvesting communication systems with battery imperfections, Journal of Communications and Networks, 14, 2, 130-139, (2012) [7] Ho, C. K.; Zhang, R., Optimal energy allocation for wireless communications with energy harvesting constraints, IEEE Transactions on Signal Processing, 60, 9, 4808-4818, (2012) · Zbl 1393.94822 [8] Huang, C.; Ho, D. W.C.; Lu, J., Partial-information-based distributed filtering in two-targets tracking sensor networks, IEEE Transactions on Circuits and Systems I. Regular Papers, 59, 4, 820-832, (2012) [9] Huang, J.; Shi, D.; Chen, T., Event-triggered state estimation with an energy harvesting sensor, IEEE Transactions on Automatic Control, 62, 9, 4768-4775, (2017) · Zbl 1390.93759 [10] Karimi, H. R., Robust $$H_\infty$$ filter design for uncertain linear systems over network with network-induced delays and output quantization, Modeling, Identification and Control, 30, 1, 27-37, (2009) [11] Knorn, S.; Dey, S., Optimal energy allocation for linear control with packet loss under energy harvesting constraints, Automatica, 77, 259-267, (2017) · Zbl 1355.93186 [12] Lei, J.; Yates, R.; Greenstein, L., A generic model for optimizing single-hop transmission policy of replenishable sensors, IEEE Transactions on Wireless Communications, 8, 2, 547-551, (2009) [13] Li, X.; Lam, J.; Gao, H.; Xiong, J., $$H_\infty$$ and $$H_2$$ filtering for linear systems with uncertain Markov transitions, Automatica, 67, 252-266, (2016) · Zbl 1335.93126 [14] Li, W.; Wei, G.; Han, F.; Liu, Y., Weighted average consensus-based unscented Kalman filtering, IEEE Transactions on Cybernetics, 46, 2, 558-567, (2016) [15] Li, L.; Xia, Y., Unscented Kalman filter over unreliable communication networks with Markovian packet dropouts, IEEE Transactions on Automatic Control, 58, 12, 3224-3230, (2013) [16] Li, Y.; Zhang, F.; Quevedo, D. E.; Lau, V.; Dey, S.; Shi, L., Power control of an energy harvesting sensor for remote state estimation, IEEE Transactions on Automatic Control, 62, 1, 277-290, (2017) · Zbl 1359.93330 [17] Liu, M.; Ho, D. W.C.; Niu, Y., Robust filtering design for stochastic system with mode-dependent output quantization, IEEE Transactions on Signal Processing, 58, 12, 6410-6416, (2010) · Zbl 1391.93248 [18] NaNacara, W.; Yaz, E. E., Recursive estimator for linear and nonlinear systems with uncertain observations, Signal Processing, 62, 2, 215-228, (1997) · Zbl 0908.93061 [19] Nayyar, A.; Başar, T.; Teneketzis, D.; Veeravalli, V. V., Optimal strategies for communication and remote estimation with an energy harvesting sensor, IEEE Transactions on Automatic Control, 58, 9, 2246-2260, (2013) · Zbl 1369.93040 [20] Niyato, D.; Hossain, E.; Rashid, M. M.; Bhargava, V. K., Wireless sensor networks with energy harvesting technologies: a game-theoretic approach to optimal energy management, IEEE Wireless Communications, 14, 4, 90-96, (2007) [21] Nourian, M.; Leong, A. S.; Dey, S., Optimal energy allocation for Kalman filtering over packet dropping links with imperfect acknowledgments and energy harvesting constraints, IEEE Transactions on Automatic Control, 59, 8, 2128-2143, (2014) · Zbl 1360.93707 [22] Ozel, O.; Tutuncuoglu, K.; Yang, J.; Ulukus, S.; Yener, A., Transmission with energy harvesting nodes in fading wireless channels: optimal policies, IEEE Journal on Selected Areas in Communications, 29, 8, 1732-1743, (2011) [23] Shen, B.; Wang, Z.; Shu, H.; Wei, G., On nonlinear $$H_\infty$$ filtering for discrete-time stochastic systems with missing measurements, IEEE Transactions on Automatic Control, 53, 9, 2170-2180, (2008) · Zbl 1367.93659 [24] Sinopoli, B.; Schenato, L.; Franceschetti, M.; Poolla, K.; Jordan, M. I.; Sastry, S. S., Kalman filtering with intermittent observations, IEEE Transactions on Automatic Control, 49, 9, 1453-1464, (2004) · Zbl 1365.93512 [25] Sudevalayam, S.; Kulkarni, P., Energy harvesting sensor nodes: Survey and implications, IEEE Communications Surveys & Tutorials, 13, 3, 443-461, (2011), Third quarter [26] Theodor, Y.; Shaked, U., Robust discrete-time minimum-variance filtering, IEEE Transactions on Signal Processing, 44, 2, 181-189, (1996) [27] Tian, E.; Wong, W. K.; Yue, D.; Yang, T. C., $$H_\infty$$ filtering for discrete-time switched systems with known sojourn probabilities, IEEE Transactions on Automatic Control, 60, 9, 2446-2451, (2015) · Zbl 1360.93230 [28] Tutuncuoglu, K.; Yener, A., Optimum transmission policies for battery limited energy harvesting nodes, IEEE Transactions on Wireless Communications, 11, 3, 1180-1189, (2012) [29] Ulukus, S.; Yener, A.; Erkip, E.; Simeone, O.; Zorzi, M.; Grover, P., Energy harvesting wireless communications: a review of recent advances, IEEE Journal on Selected Areas in Communications, 33, 3, 360-381, (2015) [30] Wu, L.; Shi, P.; Gao, H.; Wang, C., $$H_\infty$$ filtering for 2D Markovian jump systems, Automatica, 44, 7, 1849-1858, (2008) · Zbl 1149.93346 [31] Yang, J.; Ulukus, S., Optimal packet scheduling in an energy harvesting communication system, IEEE Transactions on Communications, 60, 1, 220-230, (2012) [32] Zhang, X. M.; Han, Q. L., Event-based $$H_\infty$$ filtering for sampled-data systems, Automatica, 51, 55-69, (2015) · Zbl 1309.93096
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.