Uniting Observers

We propose a framework for designing observers possessing global convergence properties and desired asymptotic behaviors for the state estimation of nonlinear systems. The proposed scheme consists in combining two given continuous-time observers: One, denoted as global, ensures (approximate) convergence of the estimation error for any initial condition ranging in some prescribed set, while the other, denoted as local, guarantees a desired local behavior. We make assumptions on the properties of these two observers, and not on their structures, and then explain how to unite them as a single scheme using hybrid techniques. Two case studies are provided to demonstrate the applicability of the framework. Finally, a numerical example is presented.

[1]  Konrad Reif,et al.  An EKF-Based Nonlinear Observer with a Prescribed Degree of Stability , 1998, Autom..

[2]  Denis V. Efimov,et al.  Interval state observer for nonlinear time varying systems , 2013, Autom..

[3]  Romain Postoyan,et al.  A multi-observer approach for the state estimation of nonlinear systems , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[4]  Daniele Astolfi,et al.  Integral Action in Output Feedback for Multi-Input Multi-Output Nonlinear Systems , 2015, IEEE Transactions on Automatic Control.

[5]  Daniele Astolfi,et al.  Uniting local and global observers for the state estimation of nonlinear continuous-time systems , 2017, 2017 IEEE 56th Annual Conference on Decision and Control (CDC).

[6]  Eduardo Sontag,et al.  Output-to-state stability and detectability of nonlinear systems , 1997 .

[7]  Daniele Astolfi,et al.  Design of local observers for autonomous nonlinear systems not in observability canonical form , 2019, Autom..

[8]  Eduardo D. Sontag,et al.  Input-Output-to-State Stability , 2001, SIAM J. Control. Optim..

[9]  J. Gauthier,et al.  Deterministic Observation Theory and Applications , 2001 .

[10]  Nicolas Boizot,et al.  An adaptive high-gain observer for nonlinear systems , 2010, Autom..

[11]  Gildas Besancon,et al.  Nonlinear observers and applications , 2007 .

[12]  Hassan K. Khalil,et al.  High-gain observers in nonlinear feedback control , 2009, 2009 IEEE International Conference on Control and Automation.

[13]  Chaohong Cai,et al.  Characterizations of input-to-state stability for hybrid systems , 2009, Syst. Control. Lett..

[14]  Jean-Jacques E. Slotine,et al.  A Contraction Theory-Based Analysis of the Stability of the Deterministic Extended Kalman Filter , 2015, IEEE Transactions on Automatic Control.

[15]  Christopher Edwards,et al.  Sliding Mode Control and Observation , 2013 .

[16]  Daniele Astolfi,et al.  High-gain observers with limited gain power for systems with observability canonical form , 2017, Autom..

[17]  A. Krener,et al.  A hybrid computational approach to nonlinear estimation , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[18]  Hyungbo Shim,et al.  Nonlinear observer design via passivation of error dynamics , 2003, Autom..

[19]  Petar V. Kokotovic,et al.  Nonlinear observers: a circle criterion design and robustness analysis , 2001, Autom..

[20]  Ricardo G. Sanfelice,et al.  On the performance of high-gain observers with gain adaptation under measurement noise , 2011, Autom..

[21]  L. Marconi,et al.  A High-Gain Nonlinear Observer With Limited Gain Power , 2015, IEEE Transactions on Automatic Control.

[22]  Christophe Prieur.  Uniting Local and Global Controllers with Robustness to Vanishing Noise , 2001, Math. Control. Signals Syst..

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

[24]  Gilles Duc,et al.  An interpolation method for gain-scheduling , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[25]  Graham C. Goodwin,et al.  Fundamental Limitations in Filtering and Control , 1997 .

[26]  Daniele Astolfi,et al.  Low-power peaking-free high-gain observers , 2018, Autom..

[27]  Vincent Andrieu,et al.  On the Existence of a Kazantzis--Kravaris/Luenberger Observer , 2006, SIAM J. Control. Optim..

[28]  Andrew R. Teel,et al.  Uniting Local and Global Output Feedback Controllers , 2011, IEEE Transactions on Automatic Control.

[29]  Ali Zemouche,et al.  On LMI conditions to design observers for Lipschitz nonlinear systems , 2013, Autom..

[30]  Salim Ibrir,et al.  On observer design for nonlinear systems , 2006, Int. J. Syst. Sci..

[31]  A. Krener.  The Convergence of the Extended Kalman Filter , 2002, math/0212255.

[32]  L. Praly,et al.  Uniting local and global controllers , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[33]  Romain Postoyan,et al.  Local observers design for a class of neural mass models , 2015, 2015 European Control Conference (ECC).

[34]  Richard M. Murray,et al.  Uniting local and global controllers for the Caltech ducted fan , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).