Robust output feedback stabilization of nonlinear networked systems via a finite data-rate communication channel

This paper addresses a robust stabilization problem of a class of uncertain nonlinear systems using output measurements via a finite data-rate communication channel. The authors assumes that there exist an observer and a control law for the systems in the absence of any finite data-rate communication channel. Based on the observer and the control law, the authors constructs an encoder/decoder pair and provides a sufficient condition, including suitable sampling period and data rate, which will guarantee the stability of the closed-loop systems when a finite data-rate communication channel is introduced.

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

[2]  Andrey V. Savkin,et al.  Analysis and synthesis of networked control systems: Topological entropy, observability, robustness and optimal control , 2005, Autom..

[3]  Robin J. Evans,et al.  Topological feedback entropy and Nonlinear stabilization , 2004, IEEE Transactions on Automatic Control.

[4]  Bruce A. Francis,et al.  Limited Data Rate in Control Systems with Networks , 2002 .

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

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

[7]  C. De Persis,et al.  On stabilization of nonlinear systems under data rate constraints using output measurements , 2006 .

[8]  Andrey V. Savkin,et al.  Qualitative Theory of Hybrid Dynamical Systems , 2012 .

[9]  Andrey V. Savkin,et al.  Output feedback stabilization of nonlinear networked control systems with non-decreasing nonlinearities: a matrix inequalities approach , 2007 .

[10]  Eduardo Sontag,et al.  Changing supply functions in input/state stable systems , 1995, IEEE Trans. Autom. Control..

[11]  Andrey V. Savkin,et al.  Detectability and Output Feedback Stabilizability of Nonlinear Networked Control Systems , 2007, Proceedings of the 44th IEEE Conference on Decision and Control.

[12]  Yuanqing Xia,et al.  Analysis and Synthesis of Networked Control Systems , 2011 .

[13]  Ian R. Petersen,et al.  Robust stabilization of linear uncertain discrete-time systems via a limited capacity communication channel , 2004, Syst. Control. Lett..

[14]  R. Rajamani,et al.  Existence and design of observers for nonlinear systems: Relation to distance to unobservability , 1998 .

[15]  G. Sallet,et al.  Observers for Lipschitz non-linear systems , 2002 .

[16]  Andrey V. Savkin,et al.  The problem of LQG optimal control via a limited capacity communication channel , 2004, Syst. Control. Lett..

[17]  I. Petersen,et al.  Multi-rate stabilization of multivariable discrete-time linear systems via a limited capacity communication channel , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[18]  Robin J. Evans,et al.  Hybrid Dynamical Systems: Controller and Sensor Switching Problems , 2012 .

[19]  Andrey V. Savkin,et al.  Decentralized robust set-valued state estimation in networked multiple sensor systems , 2010, Comput. Math. Appl..

[20]  Alberto Isidori,et al.  Stabilizability by state feedback implies stabilizability by encoded state feedback , 2004, Syst. Control. Lett..

[21]  Claudio De Persis,et al.  Nonlinear stabilizability via encoded feedback: The case of integral ISS systems , 2006, Autom..

[22]  A. Matveev,et al.  Estimation and Control over Communication Networks , 2008 .

[23]  Bongsob Song,et al.  Observer-based dynamic surface control for a class of nonlinear systems: an LMI approach , 2004, IEEE Transactions on Automatic Control.