Observer-based Adaptive Fuzzy Control for a Class of Nonlinear Time-delay Systems

An observer-based adaptive fuzzy control is presented for a class of nonlinear systems with unknown time delays. The state observer is first designed, and then the controller is designed via the adaptive fuzzy control method based on the observed states. Both the designed observer and controller are independent of time delays. Using an appropriate Lyapunov-Krasovskii functional, the uncertainty of the unknown time delay is compensated, and then the fuzzy logic system in Mamdani type is utilized to approximate the unknown nonlinear functions. Based on the Lyapunov stability theory, the constructed observer-based controller and the closed-loop system are proved to be asymptotically stable. The designed control law is independent of the time delays and has a simple form with only one adaptive parameter vector, which is to be updated on-line. Simulation results are presented to demonstrate the effectiveness of the proposed approach.

[1]  Qing-Guo Wang,et al.  Delay-range-dependent stability for systems with time-varying delay , 2007, Autom..

[2]  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..

[3]  Xin Sun,et al.  An improved approach to delay-dependent robust stabilization for uncertain singular time-delay systems , 2010, Int. J. Autom. Comput..

[4]  M. Hamdy.  State Observer Based Dynamic Fuzzy Logic System for a Class of SISO Nonlinear Systems , 2013, Int. J. Autom. Comput..

[5]  Licheng Jiao,et al.  Adaptive NN Backstepping Output-Feedback Control for Stochastic Nonlinear Strict-Feedback Systems With Time-Varying Delays , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[6]  H. Yousef,et al.  Adaptive Mamdani fuzzy control for a class of nonlinear time-delays systems , 2009, 2009 International Conference on Computer Engineering & Systems.

[7]  Junmin Li,et al.  Adaptive neural control for a class of nonlinearly parametric time-delay systems , 2005, IEEE Transactions on Neural Networks.

[8]  Min Wang,et al.  Adaptive fuzzy control of nonlinear time-delay systems , 2008, 2008 Chinese Control and Decision Conference.

[9]  Weisheng Chen,et al.  Globally stable adaptive backstepping fuzzy control for output-feedback systems with unknown high-frequency gain sign , 2010, Fuzzy Sets Syst..

[10]  Shuzhi Sam Ge,et al.  Practical adaptive neural control of nonlinear systems with unknown time delays , 2005, Proceedings of the 2004 American Control Conference.

[11]  Shengyuan Xu,et al.  Technical communique: New results on delay-dependent robust H∞ control for systems with time-varying delays , 2006 .

[12]  Jie Yang,et al.  Adaptive control for a class of nonlinear systems with time-varying delays in state and input , 2011 .

[13]  Mohamed Hamdy,et al.  Adaptive Mamdani Fuzzy Backstepping Control for a Class of Strict-feedback Nonlinear Time-varying Delay Systems , 2010 .

[14]  Peng Shi,et al.  Robust backstepping control for a class of time delayed systems , 2005, IEEE Transactions on Automatic Control.

[15]  Li-Xin Wang,et al.  Adaptive fuzzy systems and control - design and stability analysis , 1994 .

[16]  El Houssaine Tissir,et al.  Delay Dependent Robust Stability of Singular Systems with Additive Time-varying Delays , 2013, Int. J. Autom. Comput..

[17]  Shaocheng Tong,et al.  Observer-Based Adaptive Fuzzy Backstepping Control for a Class of Stochastic Nonlinear Strict-Feedback Systems , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[18]  X. Liu,et al.  Adaptive Neural Control of Pure-Feedback Nonlinear Time-Delay Systems via Dynamic Surface Technique , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[19]  Yong He,et al.  Stability Analysis and Robust Control of Time-Delay Systems , 2010 .

[20]  Tao Zhang,et al.  A direct adaptive controller for dynamic systems with a class of nonlinear parameterizations , 1999, Autom..

[21]  Mohamed Hamdy,et al.  Adaptive Fuzzy-Based Tracking Control for a Class of Strict-Feedback SISO nonlinear Time-Delay Systems without backstepping , 2012, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[22]  Y. Cao,et al.  Robust stabilization of uncertain systems with time-varying multistate delay , 1998, IEEE Trans. Autom. Control..