Output feedback control of a class of feedforward nonlinear systems in the presence of sensor noise

SUMMARY We propose an output feedback controller for a class of feedforward nonlinear systems under sensor noise. The sensor noise is any signal whose DC component is finite, which covers not only deterministic signals but also random signals including many practical noises. We introduce a notion of virtual state, then propose a measurement output feedback controller that utilizes a gain scaling factor. The gain scaling factor is commonly employed by the observer and controller. Through analysis, we show that all system states and output remain to be bounded in the presence of sensor noise, and the bound of states except output can be made arbitrarily small. Moreover, if the DC component of sensor noise is zero, the ultimate bound of the states and output can be made arbitrarily small by increasing the gain scaling factor in the presence of sensor noise. Copyright © 2013 John Wiley & Sons, Ltd.

[1]  Fuzhen Zhang.  The Schur complement and its applications , 2005 .

[2]  C. W. Chan,et al.  Noise attenuation of compensators for rate and amplitude constrained systems , 1999, Autom..

[3]  Riccardo Marino,et al.  Adaptive tracking and disturbance rejection for uncertain nonlinear systems , 2005, IEEE Transactions on Automatic Control.

[4]  Emanuele Garone,et al.  Switching control laws in the presence of measurement noise , 2010, Syst. Control. Lett..

[5]  Zhong-Ping Jiang,et al.  Robust control of uncertain nonlinear systems via measurement feedback , 1999, IEEE Trans. Autom. Control..

[6]  Stefano Battilotti.  Stochastic stabilization of nonlinear systems in feedforward form with noisy outputs , 2005, IEEE Transactions on Automatic Control.

[7]  Qing Wei Jia,et al.  Disturbance Rejection Through Disturbance Observer With Adaptive Frequency Estimation , 2009, IEEE Transactions on Magnetics.

[8]  Lihua Xie,et al.  Robust filtering for 2-D discrete-time linear systems with convex-bounded parameter uncertainty , 2010, Autom..

[9]  Jong-Tae Lim,et al.  Global exponential stabilization of a class of nonlinear systems by output feedback , 2005, IEEE Trans. Autom. Control..

[10]  Jie Huang,et al.  Global Robust Output Regulation by State Feedback for Strict Feedforward Systems , 2009, IEEE Transactions on Automatic Control.

[11]  M. P. Tzamtzi,et al.  An explicit formula of bounded feedback stabilizers for feedforward systems , 2001, Syst. Control. Lett..

[12]  Miroslav Krstic,et al.  Input Delay Compensation for Forward Complete and Strict-Feedforward Nonlinear Systems , 2010, IEEE Transactions on Automatic Control.

[13]  Reza Olfati-Saber,et al.  Nonlinear control of underactuated mechanical systems with application to robotics and aerospace vehicles , 2001 .

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

[15]  Lorenzo Marconi,et al.  Stabilization of nonlinear feedforward systems: a robust approach , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[16]  Jong-Tae Lim,et al.  Measurement feedback control for a class of feedforward nonlinear systems , 2013 .

[17]  Prashanth Krishnamurthy,et al.  Generalized State Scaling and Applications to Feedback, Feedforward, and Nontriangular Nonlinear Systems , 2007, IEEE Transactions on Automatic Control.

[18]  Hassan K. Khalil,et al.  High-gain observers in the presence of measurement noise: A switched-gain approach , 2009, Autom..

[19]  Zhengtao Ding.  Adaptive estimation and rejection of unknown sinusoidal disturbances in a class of non-minimum-phase nonlinear systems , 2006 .

[20]  Jie Huang,et al.  A small gain approach to global stabilization of nonlinear feedforward systems with input unmodeled dynamics , 2010, Autom..

[21]  Jong-Tae Lim,et al.  Stabilisation of non-linear systems with unknown growth rate by adaptive output feedback , 2010, Int. J. Syst. Sci..

[22]  Zhiyong Chen,et al.  A Remark on Sensor Disturbance Rejection of Nonlinear Systems , 2009, IEEE Transactions on Automatic Control.

[23]  Zhi-Hong Guan,et al.  Tracking under additive white Gaussian noise effect , 2009, 2009 7th Asian Control Conference.

[24]  Sabine Mondié,et al.  Global asymptotic stabilization of feedforward systems with delay in the input , 2004, IEEE Transactions on Automatic Control.

[25]  Lorenzo Marconi,et al.  Robust asymptotic stabilization of nonlinear systems with non-hyperbolic zero dynamics: Part II , 2008, 2008 47th IEEE Conference on Decision and Control.

[26]  Giorgio Bartolini,et al.  An improved second-order sliding-mode control scheme robust against the measurement noise , 2004, IEEE Transactions on Automatic Control.

[27]  Miroslav Krstic,et al.  Feedback linearizability and explicit integrator forwarding controllers for classes of feedforward systems , 2004, IEEE Transactions on Automatic Control.