A Framework for the Observer Design for Networked Control Systems

This technical note proposes a framework for the observer design for networked control systems (NCS) affected by disturbances, via an emulation-like approach. The proposed model formulation allows us to consider various static and dynamic time-scheduling protocols, in-network processing implementations and encompasses sampled-data systems as a particular case. Provided that the continuous-time observer is robust to the measurement errors (in an appropriate sense) we derive bounds on the maximum allowable transmission interval that ensure the convergence of the observation errors under network-induced communication constraints. The stability analysis is trajectory-based and utilizes small-gain arguments. A number of observers can be combined and used within our approach to obtain estimators for NCS.

[1]  J. Gauthier,et al.  A simple observer for nonlinear systems applications to bioreactors , 1992 .

[2]  Tarek Ahmed-Ali,et al.  Observers for classes of nonlinear networked systems , 2009, 2009 6th International Multi-Conference on Systems, Signals and Devices.

[3]  Lei Zhang,et al.  Stabilization of Networked Control Systems: Designing Effective Communication Sequences , 2005 .

[4]  Geir E. Dullerud,et al.  An LMI solution to the robust synthesis problem for multi-rate sampled-data systems , 2001, Autom..

[5]  Kristi A. Morgansen,et al.  Limited communication control , 1999 .

[6]  Dragan Nesic,et al.  Observer design for linear networked control systems using matrix inequalities , 2007, 2007 46th IEEE Conference on Decision and Control.

[7]  R. Rajamani.  Observers for Lipschitz nonlinear systems , 1998, IEEE Trans. Autom. Control..

[8]  Dragan B. Daÿ.  Observer Design for Linear Networked Control Systems using Matrix Inequalities , 2007 .

[9]  Dragan Nesic,et al.  On emulation-based observer design for networked control systems , 2010, 49th IEEE Conference on Decision and Control (CDC).

[10]  Romain Postoyan,et al.  A framework for the observer design for networked control systems , 2010, Proceedings of the 2010 American Control Conference.

[11]  Dragan Nesic,et al.  A framework for nonlinear sampled-data observer design via approximate discrete-time models and emulation , 2004, Autom..

[12]  Bruce A. Francis,et al.  Stabilization with control networks , 2002, Autom..

[13]  Romain Postoyan.  Commande et construction d’observateurs pour des systèmes non linéaires incertains à données échantillonnées et en réseau , 2009 .

[14]  Mohammed M'Saad,et al.  Observer design for a class of MIMO nonlinear systems , 2004, Autom..

[15]  Richard M. Murray,et al.  On a stochastic sensor selection algorithm with applications in sensor scheduling and sensor coverage , 2006, Autom..

[16]  João Pedro Hespanha,et al.  Stabilization of nonlinear systems with limited information feedback , 2005, IEEE Transactions on Automatic Control.

[17]  P. Olver.  Nonlinear Systems , 2013 .

[18]  Iasson Karafyllis,et al.  From Continuous-Time Design to Sampled-Data Design of Observers , 2009, IEEE Transactions on Automatic Control.

[19]  Zhong-Ping Jiang,et al.  Small-gain theorem for ISS systems and applications , 1994, Math. Control. Signals Syst..

[20]  Dragan Nesic,et al.  A Unified Framework for Design and Analysis of Networked and Quantized Control Systems , 2009, IEEE Transactions on Automatic Control.

[21]  Dragan Nesic,et al.  Input-output stability properties of networked control systems , 2004, IEEE Transactions on Automatic Control.

[22]  Linda Bushnell,et al.  Asymptotic behavior of nonlinear networked control systems , 2001, IEEE Trans. Autom. Control..

[23]  Eduardo Sontag,et al.  Forward Completeness, Unboundedness Observability, and their Lyapunov Characterizations , 1999 .

[24]  Dragan Nesic,et al.  Observer design for wired linear networked control systems using matrix inequalities , 2008, Autom..

[25]  Daniel Liberzon,et al.  On stabilization of linear systems with limited information , 2003, IEEE Trans. Autom. Control..