Output Control of Nonlinear Systems with Unmodelled Dynamics1

Abstract In this paper we consider the problem of output control of nonlinear systems in the presence of structural disturbances caused by so called unmodelled dynamics. This paper develops results published in Bobtsov (2002). In Bobtsov (2002) conditions of efficiency of consecutive compensator were found for the case of output stabilization of linear parametrically uncertain plant under conditions of unmodelled asymptotically stable dynamics. We added disturbances as smooth nonlinear function meeting the conditions of sector restriction to the model and synthesized regulator for this case.

[1]  Liming Wang,et al.  A Remark on Singular Perturbations of Strongly Monotone Systems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[2]  Alexey A. Bobtsov.  Robust Output-Control for a Linear System with Uncertain Coefficients , 2002 .

[3]  Alexander L. Fradkov,et al.  ADAPTIVE OUTPUT CONTROL METHODS FOR NONLINEAR OBJECTS , 1996 .

[4]  Eduardo D. Sontag,et al.  Almost Global Convergence in Singular Perturbations of Strongly Monotone Systems , 2006 .

[5]  Nan-Chyuan Tsai,et al.  Digital sliding mode control for Maglev rotors , 2006, 2006 American Control Conference.

[6]  Desineni S Naidu,et al.  Singular perturbations and time scales in control theory and applications: An overview , 2002 .

[7]  Alexander L. Fradkov,et al.  Speed-gradient control of energy in singularly perturbed systems , 2004 .

[8]  Yun Zou,et al.  Output feedback finite frequency H∞ control for SISO singularly perturbed systems , 2009, 2009 7th Asian Control Conference.

[9]  Dusan M. Stipanovic,et al.  Multi-Agent Formation Control and Trajectory Tracking via Singular Perturbation , 2007, 2007 IEEE International Conference on Control Applications.

[10]  Chunyu Yang,et al.  Multiobjective Control for T–S Fuzzy Singularly Perturbed Systems , 2009, IEEE Transactions on Fuzzy Systems.

[11]  N. Berglund,et al.  Noise-Induced Phenomena in Slow-Fast Dynamical Systems: A Sample-Paths Approach , 2005 .

[12]  Xiaomei Zhang,et al.  On the model-based networked control for singularly perturbed systems with nonlinear uncertainties , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[13]  Alexey A. Bobtsov,et al.  Fradkov theorem-based design of the control of nonlinear systems with functional and parametric uncertainties , 2005 .

[14]  Hassan K. Khalil,et al.  Singular perturbation methods in control : analysis and design , 1986 .

[15]  Liming Wang,et al.  Singularly Perturbed Monotone Systems and an Application to Double Phosphorylation Cycles , 2008, J. Nonlinear Sci..

[16]  Thang Nguyen,et al.  Solving the singularly perturbed matrix differential Riccati equation: A Lyapunov equation approach , 2010, Proceedings of the 2010 American Control Conference.

[17]  Tewfik Sari,et al.  Singular Perturbation Methods in Control Theory , 2006 .

[18]  Liming Wang,et al.  Further results on singularly perturbed monotone systems, with an application to double phosphorylation cycles , 2007, 2007 46th IEEE Conference on Decision and Control.

[19]  Alexander L. Fradkov,et al.  Nonlinear and Adaptive Control of Complex Systems , 1999 .

[20]  A. Fradkov,et al.  Singular perturbations of systems controlled by energy-speed-gradient method , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[21]  Naira Hovakimyan,et al.  L1 adaptive controller for systems in the presence of unmodelled actuator dynamics , 2007, 2007 46th IEEE Conference on Decision and Control.

[22]  Tzuu-Hseng S. Li,et al.  Composite Fuzzy Control of Nonlinear Singularly Perturbed Systems , 2007, IEEE Transactions on Fuzzy Systems.