On Feedback Capability in a Class of Nonlinearly Parameterized Uncertain Systems

In this technical note, we will investigate the maximum capability and limitations of the feedback mechanism in globally stabilizing a basic class of discrete-time nonlinearly parameterized dynamical systems with multiple unknown parameters. Both “possibility” and “impossibility” theorems together with a fairly complete characterization on the capability of feedback will be presented. It will be seen that to characterize the feedback capability, the growth rates of the sensitivity functions of the nonlinear dynamics with respect to the uncertain parameters play a crucial role, and a suitable decomposition of the family of the nonlinearly parameterized functions in question turns out to be necessary.

[1]  Lei Guo,et al.  A new critical theorem for adaptive nonlinear stabilization , 2010, Autom..

[2]  Anuradha M. Annaswamy,et al.  Adaptive control of nonlinearly parameterized systems with a triangular structure , 2002, Autom..

[3]  Shinji Hara,et al.  Feedback control synthesis of multiple frequency domain specifications via generalized KYP lemma , 2007 .

[4]  Xue Feng.  ON LIMITATIONS OF THE SAMPLED-DATA FEEDBACK FOR NONPARAMETRIC DYNAMICAL SYSTEMS , 2002 .

[5]  Graham C. Goodwin,et al.  Adaptive filtering prediction and control , 1984 .

[6]  XUEFeng,et al.  ON LIMITATIONS OF THE SAMPLED—DATA FEEDBACK FOR NONPARAMETRIC DYNAMICAL SYSTEMS , 2002 .

[7]  Zhong-Ping Jiang,et al.  Nonlinear small-gain theorems for discrete-time feedback systems and applications , 2004, Autom..

[8]  Gang Tao,et al.  Adaptive Control of Systems with Actuator and Sensor Nonlinearities , 1996 .

[9]  George Zames,et al.  Adaptive vs robust control: Information based concepts , 1993 .

[10]  Carlos Canudas de Wit,et al.  A survey of models, analysis tools and compensation methods for the control of machines with friction , 1994, Autom..

[11]  Lei Guo,et al.  A dynamical inequality for the output of uncertain nonlinear systems , 2012, Science China Information Sciences.

[12]  Lennart Ljung,et al.  Nonlinear black-box modeling in system identification: a unified overview , 1995, Autom..

[13]  R. Kanellakopoulos.  A discrete-time adaptive nonlinear system , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[14]  Anuradha M. Annaswamy,et al.  Robust Adaptive Control , 1984, 1984 American Control Conference.

[15]  Bernard Bercu,et al.  Adaptive control of parametric nonlinear autoregressive models via a new martingale approach , 2002, IEEE Trans. Autom. Control..

[16]  R. Ortega,et al.  Some remarks on adaptive neuro-fuzzy systems , 1995, Proceedings of Tenth International Symposium on Intelligent Control.

[17]  Han-Fu Chen,et al.  Identification and Stochastic Adaptive Control , 1991 .

[18]  Bruno Portier,et al.  Nonparametric Estimation and Adaptive Control of Functional Autoregressive Models , 2000, SIAM J. Control. Optim..

[19]  Guo Lei,et al.  On adaptive stabilization of nonlinearly parameterized discrete-time systems , 2008, 2008 27th Chinese Control Conference.

[20]  Lei Guo,et al.  Fundamental limitations of discrete-time adaptive nonlinear control , 1999, IEEE Trans. Autom. Control..

[21]  Lei Guo.  On Critical Stability of Discrete-Time Adaptive Nonlinear Control , 1998 .

[22]  Robin J. Evans,et al.  Controlling nonlinear time-varying systems via euler approximations , 1992, Autom..

[23]  A. Annaswamy,et al.  Adaptive control of nonlinearly parametrized systems with a triangular structure , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[24]  Liang-Liang Xie,et al.  On robust stability of discrete-time adaptive nonlinear control , 2006, Syst. Control. Lett..

[25]  Lei Guo,et al.  How much uncertainty can be dealt with by feedback? , 2000, IEEE Trans. Autom. Control..

[26]  Lei Guo,et al.  An impossibility theorem on feedback based on stochastic embedding , 2008, 2008 47th IEEE Conference on Decision and Control.

[27]  Lei Guo,et al.  A polynomial criterion for adaptive stabilizability of discrete-time nonlinear systems , 2006, Commun. Inf. Syst..

[28]  Lei Guo,et al.  Adaptive control of discrete-time nonlinear systems with structural uncertainties , 2000 .