Output-feedback Control for a Class of Uncertain Nonlinear Systems with Linearly Unmeasured States Dependent Growth

Abstract This paper is devoted to the problem of global stabilization by output-feedback for a class of nonlinear systems with uncertain control coefficients, stable zero-dynamics, and linearly unmeasured states dependent growth. First, by introducing two kinds of appropriate state transformations, the original system is converted into a new system with deterministic virtual control coefficients and the separated zero-dynamics. Then, a suitable observer based on high-gain K-filters is constructed for the new system, and the backstepping design approach is successfully proposed to the output-feedback controller. It is shown that the global asymptotic stability of the closed-loop system can be guaranteed by the appropriate choice of the design parameters. A simulation example is also provided to show the correctness of the theoretical results and the effectiveness of the proposed approach.

[1]  Ji-Feng Zhang,et al.  Practical Output-Feedback Risk-Sensitive Control for Stochastic Nonlinear Systems with Stable Zero-Dynamics , 2006, SIAM J. Control. Optim..

[2]  Hassan K. Khalil,et al.  A separation principle for the stabilization of a class of nonlinear systems , 1997, 1997 European Control Conference (ECC).

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

[4]  Zhong-Ping Jiang,et al.  Linear output feedback with dynamic high gain for nonlinear systems , 2004, Syst. Control. Lett..

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

[6]  Laurent Praly.  Asymptotic stabilization via output feedback for lower triangular systems with output dependent incremental rate , 2003, IEEE Trans. Autom. Control..

[7]  Alessandro Astolfi,et al.  Norm estimators and global output feedback stabilization of nonlinear systems WithISS inverse dynamics , 2006, IEEE Transactions on Automatic Control.

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

[9]  W. Dayawansa,et al.  Global stabilization by output feedback: examples and counterexamples , 1994 .

[10]  Jong-Tae Lim,et al.  Stabilization of a class of nonlinear systems by adaptive output feedback , 2005, Autom..

[11]  Wei Lin,et al.  Output feedback control of a class of nonlinear systems: a nonseparation principle paradigm , 2002, IEEE Trans. Autom. Control..

[12]  Prashanth Krishnamurthy,et al.  Global adaptive output feedback tracking for nonlinear systems linear in unmeasured states , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[13]  Yungang Liu,et al.  Global stabilization by output feedback for a class of nonlinear systems with uncertain control coefficients and unmeasured states dependent growth , 2008, Science in China Series F: Information Sciences.

[14]  Miroslav Krstic,et al.  Nonlinear and adaptive control de-sign , 1995 .

[15]  Murat Arcak,et al.  Observer design for systems with multivariable monotone nonlinearities , 2003, Syst. Control. Lett..

[16]  Wei Lin,et al.  Further results on global stabilization of uncertain nonlinear systems by output feedback , 2005 .

[17]  Yungang Liu,et al.  Output feedback stabilization for stochastic nonlinear systems in observer canonical form with stable zero-dynamics , 2007, Science in China Series : Information Sciences.

[18]  Riccardo Marino,et al.  Nonlinear control design: geometric, adaptive and robust , 1995 .

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

[20]  Tzyh Jong Tarn,et al.  Exponential Observers for Nonlinear Dynamic Systems , 1975, Inf. Control..

[21]  Jie Huang,et al.  Global output feedback stabilization for uncertain nonlinear systems with output dependent incremental rate , 2004, Proceedings of the 2004 American Control Conference.