Adaptive robust stabilization of a class of uncertain non-linear systems with mismatched time-varying parameters

In this paper, an adaptive robust stabilization algorithm is presented for a class of non-linear systems with mismatched uncertainties. In this regard, a new controller based on the Lyapunov theory is proposed in order to overcome the problem of stabilizing non-linear time-varying systems with mismatched uncertainties. This method is such that the stability of the closed-loop system is guaranteed in the absence of the triangularity assumption. The proposed approach leads to asymptotic convergence of the states of the closed-loop system to zero for unknown but bounded uncertainties. Subsequently, this method is modified so that all the signals in the closed-loop system are uniformly ultimately bounded. Eventually, numerical simulations support the effectiveness of the given algorithm.

[1]  Chih-Chiang Cheng,et al.  Design of adaptive sliding mode controllers for systems with mismatched uncertainty to achieve asymptotic stability , 2010, Proceedings of the 2010 American Control Conference.

[2]  Manuel A. Duarte-Mermoud,et al.  Simplified robust adaptive control of a class of time‐varying chaotic systems , 2008 .

[3]  Hansheng Wu,et al.  Exponential stabilization of SISO nonlinear systems with uncertainties , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[4]  Marios M. Polycarpou,et al.  A Robust Adaptive Nonlinear Control Design , 1993, 1993 American Control Conference.

[5]  Yuki Hashimoto.  Robust output tracking of nonlinear systems with mismatched uncertainties , 1999 .

[6]  Leonid M. Fridman,et al.  Analysis and design of integral sliding manifolds for systems with unmatched perturbations , 2006, IEEE Transactions on Automatic Control.

[7]  Riccardo Marino,et al.  Robust stabilization of feedback linearizable time-varying uncertain nonlinear systems, , 1993, Autom..

[8]  George Leitmann,et al.  On ultimate boundedness control of uncertain systems in the absence of matching assumptions , 1982 .

[9]  Mohammad Mehdi Arefi,et al.  Adaptive robust synchronization of Rossler systems in the presence of unknown matched time-varying parameters , 2010 .

[10]  Ya-Jun Pan,et al.  Analysis and design of integral sliding mode control based on Lyapunov's direct method , 2003, Proceedings of the 2003 American Control Conference, 2003..

[11]  J. Yan,et al.  Adaptive chattering free variable structure control for a class of chaotic systems with unknown bounded uncertainties , 2005 .

[12]  Hansheng Wu,et al.  Exponential stability of a class of nonlinear dynamical systems with uncertainties , 1993 .

[13]  Wen-Jun Cao,et al.  Nonlinear integral-type sliding surface for both matched and unmatched uncertain systems , 2004, IEEE Trans. Autom. Control..

[14]  Z. Qu.  Global stabilization of nonlinear systems with a class of unmatched uncertainties , 1992, [Proceedings 1992] The First IEEE Conference on Control Applications.

[15]  Gilbert Strang,et al.  Introduction to applied mathematics , 1988 .

[16]  Mohammad Mahdi Arefi,et al.  Adaptive Robust control of Hyperchaotic Rossler system in the presence of matching disturbance , 2009 .

[17]  Riccardo Marino,et al.  Nonlinear control design: geometric, adaptive and robust , 1995 .

[18]  M. Corless,et al.  Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems , 1981 .

[19]  Zhihua Qu.  Asymptotic Stability of Controlling Uncertain Dynamical Systems , 1992, 1992 American Control Conference.

[20]  G. Leitmann,et al.  Robustness of uncertain systems in the absence of matching assumptions , 1987 .