×

Two triggered information transmission algorithms for distributed moving horizon state estimation. (English) Zbl 1285.93095

Summary: In this work, we consider the reduction of information transmission frequency of Distributed Moving Horizon Estimation (DMHE) for a class of nonlinear systems in which interacting subsystems exchange information with each other through a shared communication network. Specifically, algorithms based on two event-triggered methods are proposed to reduce the number of information transmissions between the subsystems in a DMHE scheme. In the first algorithm, a subsystem sends out its current information when a triggering condition based on the difference between the current state estimate and a previously transmitted one is satisfied; in the second algorithm, the transmission of information from a subsystem to other subsystems is triggered by the difference between the current measurement of the output and its derivatives and a previously transmitted measurement. In order to ensure the convergence and ultimate boundedness of the estimation error, we also propose to redesign the local moving horizon estimator of a subsystem to account for the possible lack of state updates from other subsystems explicitly. A chemical process is utilized to demonstrate the applicability and performance of the proposed approaches.

MSC:

93E10 Estimation and detection in stochastic control theory
93E25 Computational methods in stochastic control (MSC2010)
93C10 Nonlinear systems in control theory
Full Text: DOI

References:

[1] Scattolini, R., Architectures for distributed and hierarchical model predictive control—a review, J. Process Control, 19, 723-731 (2009)
[2] Christofides, P. D.; Liu, J.; Muñoz de la Peña, D., (Networked and Distributed Predictive Control: Methods and Nonlinear Process Network Applications. Networked and Distributed Predictive Control: Methods and Nonlinear Process Network Applications, Advances in Industrial Control Series (2011), Springer-Verlag: Springer-Verlag London, England), 230 · Zbl 1304.93002
[3] Liu, J.; Muñoz de la Peña, D.; Christofides, P. D., Distributed model predictive control of nonlinear process systems, AIChE J., 55, 1171-1184 (2009)
[4] Liu, J.; Chen, X.; Muñoz de la Peña, D.; Christofides, P. D., Sequential and iterative architectures for distributed model predictive control of nonlinear process systems, AIChE J., 56, 2137-2149 (2010)
[5] Soroush, M., State and parameter estimations and their applications in process control, Comput. Chem. Eng., 23, 229-245 (1998)
[6] Kazantzis, N.; Kravaris, C., Nonlinear observer design using Lyapunov’s auxiliary theorem, Systems Control Lett., 34, 241-247 (1998) · Zbl 0909.93002
[7] Dochain, D., State and parameter estimation in chemical and biochemical processes: a tutorial, J. Process Control, 13, 801-818 (2003)
[8] Liu, J., Moving horizon state estimation for nonlinear systems with bounded uncertainties, Chem. Eng. Sci., 93, 376-386 (2013)
[9] Subbotin, M. V.; Smith, R. S., Design of distributed decentralized estimators for formations with fixed and stochastic communication topologies, Automatica, 45, 2491-2501 (2009) · Zbl 1183.93123
[10] Chen, B.; Wang, W., Robust stabilization of nonlinearly perturbed large-scale systems by decentralized observer-controller compensators, Automatica, 26, 1041-1305 (1990) · Zbl 0717.93045
[11] Antonelli, G.; Arrichiello, F.; Caccavale, F.; Marino, A., A decentralized controller-observer scheme for multi-agent weighted centroid tracking, IEEE Trans. Automat. Control, 58, 1310-1316 (2013) · Zbl 1369.93009
[12] Mutambara, A. G.O.; Durrant-Whyte, H. E., Estimation and control for a modular wheeled mobile robot, IEEE Trans. Control Syst. Technol., 8, 35-46 (2000)
[13] Khan, U. A.; Moura, J. M.F., Distributing the Kalman filter for large-scale systems, IEEE Trans. Signal Process., 56, 4919-4935 (2008) · Zbl 1390.94242
[14] Stanković, S. S.; Stanković, M. S.; Stipanović, D. M., Consensus based overlapping decentralized estimation with missing observations and communication faults, Automatica, 45, 1397-1406 (2009) · Zbl 1166.93374
[15] Farina, M.; Ferrari-Trecate, G.; Scattolini, R., Distributed moving horizon estimation for linear constrained systems, IEEE Trans. Automat. Control, 55, 11, 2462-2475 (2010) · Zbl 1368.93677
[16] Farina, M.; Ferrari-Trecate, G.; Scattolini, R., Distributed moving horizon estimation for nonlinear constrained systems, Internat. J. Robust Nonlinear Control, 22, 123-143 (2012) · Zbl 1244.93008
[17] Farina, M.; Ferrari-Trecate, G.; Scattolini, R., Moving-horizon partition-based state estimation of large-scale systems, Automatica, 46, 910-918 (2010) · Zbl 1191.93130
[18] Farina, M.; Ferrari-Trecate, G.; Scattolini, R., Moving horizon estimation for distributed nonlinear systems with application to cascade river reaches, J. Process Control, 21, 767-774 (2011)
[20] Rao, C. V.; Rawlings, J. B.; Lee, J. H., Constrained linear state estimation—a moving horizon approach, Automatica, 37, 1619-1628 (2001) · Zbl 0998.93039
[21] Zhang, J.; Liu, J., Distributed moving horizon estimation for nonlinear systems with bounded uncertainties, J. Process Control, 23, 1281-1295 (2013)
[22] Tabuada, P., Event-triggered real-time scheduling of stabilizing control tasks, IEEE Trans. Automat. Control, 52, 1680-1685 (2007) · Zbl 1366.90104
[23] Anta, A.; Tabuada, P., To sample or not to sample: self-triggered control for nonlinear systems, IEEE Trans. Automat. Control, 55, 2030-2042 (2010) · Zbl 1368.93355
[28] Lemmon, M., Event-triggered feedback in control, estimation, and optimization, (Bemporad, A.; Heemels, M. H.; Johansson, M., Networked Control Systems. Networked Control Systems, LNCIS, vol. 406 (2010), Springer-Verlag: Springer-Verlag Berlin), 293-359 · Zbl 1216.93055
[29] Sun, Y.; El-Farra, N. H., Quasi-decentralized model-based networked control of process systems, Comput. Chem. Eng., 32, 2016-2029 (2008)
[31] Zhang, J.; Liu, J., Lyapunov-based mpc with robust moving horizon estimation and its triggered implementation, AIChE J., 59, 4273-4286 (2013)
[32] Visioli, A., Practical PID Control (2006), Springer · Zbl 1122.93032
[33] Chartrand, R., Numerical differentiation of noisy, nonsmooth data, ISRN Appl. Math., 2011, 11 (2011) · Zbl 1242.65045
[34] Isidori, A., Nonlinear Control Systems: An Introduction (1995), Springer-Verlag: Springer-Verlag Berlin, Heidelberg · Zbl 0569.93034
[35] Nes˘ić, D.; Teel, A.; Kokotovic, P., Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete time approximations, Systems Control Lett., 38, 259-270 (1999) · Zbl 0985.93034
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.