Stabilization of a class of nonlinear parametrized systems by a flexible switching adaptive backstepping

Abstract In this paper, we consider global adaptive feedback control of nonlinear systems with unknown parameters entering nonlinearly. Such unknown parameters are also not required to lie in a known compact set. Unlike previous results, our proposed adaptive controller is a new double dynamical switching-type controller in which the controller parameter is tuned in a flexible switching manner via a monotonically decreasing switching logic and the controller combines the traditional adaptive theorem with the switching scheme perfectly. Global stability results of the closed-loop system have been proved.

[1]  Anuradha M. Annaswamy,et al.  Adaptation in the presence of a general nonlinear parameterization: an error model approach , 1999, IEEE Trans. Autom. Control..

[2]  Hui Yang,et al.  A multiple-model MRAC scheme for multivariable systems with matching uncertainties , 2016, Inf. Sci..

[3]  Chitralekha Mahanta,et al.  Multiple models and second level adaptation for a class of nonlinear systems with nonlinear parameterization , 2014, 2014 9th International Conference on Industrial and Information Systems (ICIIS).

[4]  Lin Zhao,et al.  Fuzzy Finite-Time Command Filtered Control of Nonlinear Systems With Input Saturation , 2018, IEEE Transactions on Cybernetics.

[5]  Jong-Tae Lim,et al.  Universal control of nonlinear systems with unknown nonlinearity and growth rate by adaptive output feedback , 2011, Autom..

[6]  Petros A. Ioannou,et al.  Stability margins in adaptive mixing control via a Lyapunov-based switching criterion , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[7]  G. Bastin,et al.  Adaptive control of nonlinear systems with nonlinear parameterization , 1996 .

[8]  Dragan Nesic,et al.  Parameter and State Estimation of Nonlinear Systems Using a Multi-Observer Under the Supervisory Framework , 2014, IEEE Transactions on Automatic Control.

[9]  Liang Liu,et al.  Adaptive tracking control for a class of uncertain switched nonlinear systems , 2015, Autom..

[10]  Ming-Li Chiang,et al.  Adaptive stabilization of a class of uncertain switched nonlinear systems with backstepping control , 2014, Autom..

[11]  Yuanqing Xia,et al.  On designing of sliding-mode control for stochastic jump systems , 2006, IEEE Transactions on Automatic Control.

[12]  H. Khalil,et al.  Adaptive stabilization of a class of nonlinear systems using high-gain feedback , 1987 .

[13]  Ye Xudong.  Adaptive output-feedback control of nonlinear systems with unknown nonlinearities , 2005 .

[14]  Chong Lin,et al.  Command Filtering-Based Fuzzy Control for Nonlinear Systems With Saturation Input , 2017, IEEE Transactions on Cybernetics.

[15]  Elias B. Kosmatopoulos,et al.  Adaptive mixing control with multiple estimators , 2012 .

[16]  Dragan Nesic,et al.  Supervisory observer for parameter and state estimation of nonlinear systems using the DIRECT algorithm , 2017, 2017 IEEE 56th Annual Conference on Decision and Control (CDC).

[17]  Jong-Tae Lim,et al.  Stabilization of a class of nonlinear systems by adaptive output feedback , 2005, Autom..

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

[19]  Hassan K. Khalil,et al.  Lyapunov-based switching control of nonlinear systems using high-gain observers , 2005, Proceedings of the 2005, American Control Conference, 2005..

[20]  Wei Lin,et al.  Adaptive control of nonlinearly parameterized systems: the smooth feedback case , 2002, IEEE Trans. Autom. Control..

[21]  Chong Lin,et al.  Adaptive Fuzzy Control of Nonlinear Systems With Unknown Dead Zones Based on Command Filtering , 2018, IEEE Transactions on Fuzzy Systems.

[22]  Peter Xiaoping Liu,et al.  Adaptive Neural Output-Feedback Control for a Class of Nonlower Triangular Nonlinear Systems With Unmodeled Dynamics , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[23]  Peng Shi,et al.  Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters , 1999, IEEE Trans. Autom. Control..

[24]  Weiguo Xia,et al.  Adaptive Fuzzy Hierarchical Sliding-Mode Control for a Class of MIMO Nonlinear Time-Delay Systems With Input Saturation , 2017, IEEE Transactions on Fuzzy Systems.

[25]  El-Kébir Boukas,et al.  Robust Hinfinity state feedback control of discrete time-delay linear systems with norm-bounded uncertainty , 2000, Int. J. Syst. Sci..

[26]  Hassan K. Khalil,et al.  Logic-based switching for robust control of minimum-phase nonlinear systems , 2005, Syst. Control. Lett..

[27]  Global adaptive control of nonlinearly parametrized systems , 2003, IEEE Trans. Autom. Control..

[28]  R. Hotzel,et al.  Adaptive tracking strategy for a class of nonlinear systems , 1998, IEEE Trans. Autom. Control..

[29]  Bing Chen,et al.  Neural networks-based command filtering control of nonlinear systems with uncertain disturbance , 2018, Inf. Sci..

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