A Global Observer for Observable Autonomous Systems with Bounded Solution Trajectories

The problem of global observer design for autonomous systems is investigated in this paper. A constructive approach is presented for the explicit design of global observers for completely observable systems whose solution trajectories are bounded from any initial condition. Since the bound of a solution trajectory depends on the initial condition and is therefore not known a priori, the idea of universal control is employed to tune the observer gains on-line, achieving global asymptotic convergence of the proposed high-gain observer.

[1]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[2]  Arthur J. Krener,et al.  Linearization by output injection and nonlinear observers , 1983 .

[3]  D. Bestle,et al.  Canonical form observer design for non-linear time-variable systems , 1983 .

[4]  J. Willems,et al.  Global adaptive stabilization in the absence of information on the sign of the high frequency gain , 1984 .

[5]  A. Krener,et al.  Nonlinear observers with linearizable error dynamics , 1985 .

[6]  H. Khalil,et al.  Adaptive stabilization of a class of nonlinear systems using high-gain feedback , 1987 .

[7]  X. Xia,et al.  Nonlinear observer design by observer error linearization , 1989 .

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

[9]  Achim Ilchmann,et al.  Non-Identifier-Based High-Gain Adaptive Control , 1993 .

[10]  H. Khalil,et al.  Semiglobal stabilization of a class of nonlinear systems using output feedback , 1993, IEEE Trans. Autom. Control..

[11]  Wei Lin,et al.  Remarks on linearization of discrete-time autonomous systems and nonlinear observer design , 1995 .

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

[13]  C. Kravaris,et al.  Nonlinear observer design using Lyapunov's auxiliary theorem , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[14]  MingQing Xiao,et al.  Observers for linearly unobservable nonlinear systems , 2002, Syst. Control. Lett..

[15]  Wei Lin,et al.  Global stabilization of cascade systems by C0 partial-state feedback , 2002, IEEE Trans. Autom. Control..

[16]  MingQing Xiao,et al.  Nonlinear Observer Design in the Siegel Domain , 2002, SIAM J. Control. Optim..

[17]  Prashanth Krishnamurthy,et al.  Generalized adaptive output-feedback form with unknown parameters multiplying high output relative-degree states , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[18]  Arthur J. Krener,et al.  Locally Convergent Nonlinear Observers , 2003, SIAM J. Control. Optim..

[19]  Wei Lin,et al.  UNIVERSAL OUTPUT FEEDBACK CONTROL OF NONLINEAR SYSTEMS WITH UNKNOWN GROWTH RATE , 2005 .

[20]  Wei Lin,et al.  Universal adaptive control of nonlinear systems with unknown growth rate by output feedback , 2006, Autom..

[21]  Alessandro Astolfi,et al.  Global complete observability and output-to-state stability imply the existence of a globally convergent observer , 2006, Math. Control. Signals Syst..