Homogeneous Domination and the Decentralized Control Problem for Nonlinear System Stabilization

This chapter gives an overview of constructive techniques for nonlinear dynamic system stabilization in the face of uncertainties and limited information from sensors. Such techniques have ultimately allowed for a loosening of the restrictions on the classes of nonlinear systems that could be systematically stabilized. The schemes discussed herein have the distinct commonality of dominating and thereby cancelling the undesirable effects of additive perturbations. Output feedback stabilization of highly nonlinear systems is discussed first, with the specific decentralized control problem setting then considered in addition to the output feedback issue. The schemes outlined in this chapter can be found in their entirety in several papers by the authors, with specific publications cited where applicable.

[1]  W. P. Dayawansa,et al.  Recent Advances in The Stabilization Problem for Low Dimensional Systems , 1992 .

[2]  Hassan K. Khalil,et al.  DECENTRALIZED STABILIZATION OF INTERCONNECTED SYSTEMS USING OUTPUT FEEDBACK. , 1985 .

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

[4]  Zhong-Ping Jiang,et al.  On global output feedback stabilization of uncertain nonlinear systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[5]  C. Qian,et al.  A generalized homogeneous domination approach for global stabilization of inherently nonlinear systems via output feedback , 2007 .

[6]  Chunjiang Qian,et al.  A generalized framework for global output feedback stabilization of inherently nonlinear systems with uncertainties , 2007 .

[7]  H. L. Burmeister,et al.  W. Hahn, Stability of Motion. (Die Grundlehren der mathematischen Wissenschaften, Band 138). XII + 446 S m. 63 Fig. Berlin/Heidelberg/New York 1967. Springer‐Verlag. Preis geb. DM 72,– , 1969 .

[8]  J. Tsinias.  A theorem on global stabilization of nonlinear systems by linear feedback , 1991 .

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

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

[11]  Chunjiang Qian,et al.  Decentralized Control of Large-Scale Uncertain Nonlinear Systems by Linear Output Feedback , 2004, Commun. Inf. Syst..

[12]  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.

[13]  C. Qian,et al.  A Generalized Framework for Global Output Feedback Stabilization of Genuinely Nonlinear Systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[14]  A. Linnemann.  Decentralized control of dynamically interconnected systems , 1984 .

[15]  Petros A. Ioannou.  Decentralized adaptive control of interconnected systems , 1986 .

[16]  Chunjiang Qian,et al.  A homogeneous domination approach for global output feedback stabilization of a class of nonlinear systems , 2005, Proceedings of the 2005, American Control Conference, 2005..

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

[18]  E. Davison.  Brief paper: The decentralized stabilization and control of a class of unknown non-linear time-varying systems , 1974 .

[19]  Wei Lin,et al.  Homogeneous observers, iterative design, and global stabilization of high-order nonlinear systems by smooth output feedback , 2004, IEEE Trans. Autom. Control..

[20]  Wei Lin,et al.  Smooth output feedback stabilization of planar systems without controllable/observable linearization , 2002, IEEE Trans. Autom. Control..

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

[22]  Wolfgang Hahn,et al.  Stability of Motion , 1967 .

[23]  Zhong-Ping Jiang,et al.  Decentralized and adaptive nonlinear tracking of large-scale systems via output feedback , 2000, IEEE Trans. Autom. Control..

[24]  Da-Zhong Zheng.  Decentralized output feedback stabilization of a class of nonlinear interconnected systems , 1989 .

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

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

[27]  S. Jain,et al.  Decentralized adaptive output feedback design for large-scale nonlinear systems , 1997, IEEE Trans. Autom. Control..

[28]  Wei Lin,et al.  A continuous feedback approach to global strong stabilization of nonlinear systems , 2001, IEEE Trans. Autom. Control..

[29]  R. Marino,et al.  Dynamic output feedback linearization and global stabilization , 1991 .

[30]  A. Isidori.  Nonlinear Control Systems , 1985 .

[31]  Zongli Lin,et al.  Liapunov Functions and Stability in Control Theory. Lecture Notes in Control and Information Sciences 267 , 2002 .

[32]  W. P. Dayawansa,et al.  Asymptotic stabilization of a class of smooth two-dimensional systems , 1990 .

[33]  Chunjiang Qian,et al.  Decentralized Output Feedback Control of Interconnected Systems with High-Order Nonlinearities , 2007, 2007 American Control Conference.

[34]  Wei Lin,et al.  Recursive observer design and nonsmooth output feedback stabilization of inherently nonlinear systems , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

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

[36]  A. Bacciotti,et al.  Liapunov functions and stability in control theory , 2001 .

[37]  D. Konik,et al.  On stabilization of decentralized dynamic output feedback systems , 1984 .

[38]  M. Kawski.  Stabilization of nonlinear systems in the plane , 1989 .

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

[40]  Wei Lin,et al.  A Dual Observer Method for Global Stabilization of Nonlinear Systems with Limited and Uncertain Information , 2007, 2007 American Control Conference.

[41]  Hassan K. Khalil,et al.  Decentralized stabilization of nonlinear interconnected systems using high-gain feedback , 1982 .