Adaptive stabilization of time-delay feedforward nonlinear systems

In this paper, we consider the adaptive stabilization problem for feedforward nonlinear systems with time delays. An adaptive stabilizer is proposed. Our stabilizer takes a nested saturation feedback, and a set of switching logics is designed to tune online the saturation levels in a piecewise constant or switching manner. It has been shown that under our proposed control, all closed-loop states are bounded and asymptotic regulation is achieved.

[1]  Xudong Ye,et al.  Universal stabilization of feedforward nonlinear systems , 2003, Autom..

[2]  Changyun Wen,et al.  Adaptive Backstepping Control of Uncertain Systems with Unknown Input Time-Delay , 2008 .

[3]  João Pedro Hespanha,et al.  Supervision of integral-input-to-state stabilizing controllers , 2002, Autom..

[4]  Alberto Isidori,et al.  Trends in Control , 1995 .

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

[6]  S. Niculescu Delay Effects on Stability: A Robust Control Approach , 2001 .

[7]  Ye Xudong,et al.  Brief Universal stabilization of feedforward nonlinear systems , 2003 .

[8]  Xin-Ping Guan,et al.  Adaptive Tracking Controller Design of Nonlinear Systems With Time Delays and Unknown Dead-Zone Input , 2008, IEEE Transactions on Automatic Control.

[9]  M. Krstić Delay Compensation for Nonlinear, Adaptive, and PDE Systems , 2009 .

[10]  Daniel E. Miller,et al.  An adaptive controller which provides an arbitrarily good transient and steady-state response , 1991 .

[11]  L. Praly,et al.  Adding integrations, saturated controls, and stabilization for feedforward systems , 1996, IEEE Trans. Autom. Control..

[12]  Shuzhi Sam Ge,et al.  Robust adaptive control of nonlinear systems with unknown time delays , 2004, Proceedings of the 2004 IEEE International Symposium on Intelligent Control, 2004..

[13]  P. Kokotovic,et al.  Constructive Lyapunov stabilization of nonlinear cascade systems , 1996, IEEE Trans. Autom. Control..

[14]  A. Stephen Morse,et al.  Control Using Logic-Based Switching , 1997 .

[15]  Shuzhi Sam Ge,et al.  Adaptive dynamic surface control of nonlinear systems with unknown dead zone in pure feedback form , 2008, Autom..

[16]  A. Teel Using Saturation to Stabilize a Class of Single-Input Partially Linear Composite Systems , 1992 .

[17]  Jie Huang,et al.  Disturbance Attenuation of Feedforward Systems With Dynamic Uncertainty , 2008, IEEE Transactions on Automatic Control.

[18]  Jin Bae Park,et al.  Adaptive Dynamic Surface Control for Stabilization of Parametric Strict-Feedback Nonlinear Systems With Unknown Time Delays , 2007, IEEE Transactions on Automatic Control.

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

[20]  Alessandro Astolfi,et al.  Nonlinear control of feedforward systems with bounded signals , 2004, IEEE Transactions on Automatic Control.

[21]  A. Teel A nonlinear small gain theorem for the analysis of control systems with saturation , 1996, IEEE Trans. Autom. Control..

[22]  Ye Xudong,et al.  Logic-based switching adaptive stabilization of feedforward nonlinear systems , 1999 .

[23]  Tielong Shen,et al.  Adaptive feedback control of nonlinear time-delay systems: the LaSalle-Razumikhin-based approach , 2005, IEEE Transactions on Automatic Control.

[24]  P. Kokotovic,et al.  Global adaptive stabilization of cascade nonlinear systems , 1996, Autom..

[25]  Xudong Ye Logic-based switching adaptive stabilization of feedforward nonlinear systems , 1999, IEEE Trans. Autom. Control..

[26]  João Pedro Hespanha,et al.  Postprints from CCDC Title Hysteresis-based switching algorithms for supervisory control of uncertain systems Permalink , 2002 .

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

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