Constructive Nonlinear Internal Models for Global Robust Output Regulation and Application

This technical note focuses on an internal model construction approach. Several novel types of parameterized nonlinear internal models with certain output are proposed to be useful for achieving nonadaptive control based global robust output regulation with uncertain exosystems. That is, the globally stabilizing control for the augmented system can be done independent of adaptive stabilization control law. We also solve a cooperative global robust output regulation problem as an interesting application of the proposed internal models. In this way, we note that the hurdles can be circumvented arising in the same problem if the canonical linear internal model were used.

[1]  David J. Hill,et al.  Lyapunov formulation of ISS cyclic-small-gain in continuous-time dynamical networks , 2011, Autom..

[2]  Xinghu Wang,et al.  A Framework for Global Robust Output Regulation of Nonlinear Lower Triangular Systems With Uncertain Exosystems , 2018, IEEE Transactions on Automatic Control.

[3]  Jie Huang,et al.  Parameter convergence and minimal internal model with an adaptive output regulation problem , 2009, Autom..

[4]  Zhengtao Ding Output regulation of uncertain nonlinear systems with nonlinear exosystems , 2006, IEEE Transactions on Automatic Control.

[5]  Xudong Ye,et al.  Decentralized adaptive output regulation for a class of large-scale nonlinear systems , 2003, IEEE Trans. Autom. Control..

[6]  D. Luenberger Observers for multivariable systems , 1966 .

[7]  Jie Huang,et al.  Remarks on the robust output regulation problem for nonlinear systems , 2001, IEEE Trans. Autom. Control..

[8]  Eduardo Sontag Input to State Stability: Basic Concepts and Results , 2008 .

[9]  Robert Engel,et al.  Nonlinear observers for autonomous Lipschitz continuous systems , 2003, IEEE Trans. Autom. Control..

[10]  Jie Huang,et al.  Cooperative adaptive output regulation for a class of nonlinear uncertain multi-agent systems with unknown leader , 2013, Syst. Control. Lett..

[11]  D. Mayne Nonlinear and Adaptive Control Design [Book Review] , 1996, IEEE Transactions on Automatic Control.

[12]  Lorenzo Marconi,et al.  Semi-global nonlinear output regulation with adaptive internal model , 2001, IEEE Trans. Autom. Control..

[13]  Xinghu Wang,et al.  Global robust stabilization of nonlinear cascaded systems with integral ISS dynamic uncertainties , 2017, Autom..

[14]  David G. Luenberger Invertible solutions to the operator equation $TA-BT=C$ , 1965 .

[15]  Jie Huang,et al.  Global Output Regulation with Uncertain Exosystems , 2010 .

[16]  Lorenzo Marconi,et al.  Robust design of nonlinear internal models without adaptation , 2012, Autom..

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

[18]  Zhengtao Ding,et al.  Consensus Output Regulation of a Class of Heterogeneous Nonlinear Systems , 2013, IEEE Transactions on Automatic Control.

[19]  Alexander G. Loukianov,et al.  A Structurally Stable Globally Adaptive Internal Model Regulator for MIMO Linear Systems , 2011, IEEE Transactions on Automatic Control.

[20]  L. Marconi,et al.  Output Stabilization via Nonlinear Luenberger Observers , 2006, SIAM J. Control. Optim..

[21]  A. Isidori,et al.  Semiglobal nonlinear output regulation with adaptive internal model , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[22]  V. O. Nikiforov,et al.  Adaptive Non-linear Tracking with Complete Compensation of Unknown Disturbances , 1998, Eur. J. Control.

[23]  Lu Liu,et al.  Adaptive Cooperative Output Regulation for a Class of Nonlinear Multi-Agent Systems , 2015, IEEE Transactions on Automatic Control.

[24]  G. Kreisselmeier Adaptive observers with exponential rate of convergence , 1977 .

[25]  Riccardo Marino,et al.  Output regulation for linear systems via adaptive internal model , 2003, IEEE Trans. Autom. Control..

[26]  Hassan K. Khalil,et al.  Nonlinear output regulation with adaptive conditional servocompensator , 2012, Autom..

[27]  Nancy Kopell,et al.  Synchronization and Transient Dynamics in the Chains of Electrically Coupled Fitzhugh--Nagumo Oscillators , 2001, SIAM J. Appl. Math..

[28]  Huang Jie,et al.  AN OVERVIEW ON THE OUTPUT REGULATION PROBLEM , 2011 .

[29]  Christopher I. Byrnes,et al.  Nonlinear internal models for output regulation , 2004, IEEE Transactions on Automatic Control.

[30]  Yiguang Hong,et al.  Distributed Output Regulation of Nonlinear Multi-Agent Systems via Host Internal Model , 2014, IEEE Transactions on Automatic Control.

[31]  A. Isidori,et al.  Output regulation of nonlinear systems , 1990 .

[32]  Jie Huang,et al.  Nonlinear Output Regulation: Theory and Applications , 2004 .

[33]  Jie Huang,et al.  A general framework for tackling the output regulation problem , 2004, IEEE Transactions on Automatic Control.

[34]  Xinghu Wang,et al.  Output regulation of nonlinear output feedback systems with exponential parameter convergence , 2016, Syst. Control. Lett..

[35]  S. Sastry Nonlinear Systems: Analysis, Stability, and Control , 1999 .

[36]  Xu Dabo,et al.  Robust internal models for nonlinear output regulation with uncertain exosystems , 2016, 2016 35th Chinese Control Conference (CCC).