Robust Output Feedback Tracking Control for Time-Delay Nonlinear Systems Using Neural Network

In this paper, the problem of robust output tracking control for a class of time-delay nonlinear systems is considered. The systems are in the form of triangular structure with unmodeled dynamics. First, we construct an observer whose gain matrix is scheduled via linear matrix inequality approach. For the case that the information of uncertainties bounds is not completely available, we design an observer-based neural network (NN) controller by employing the backstepping method. The resulting closed-loop system is ensured to be stable in the sense of semiglobal boundedness with the help of changing supplying function idea. The observer and the controller designed are both independent of the time delays. Finally, numerical simulations are conducted to verify the effectiveness of the main theoretic results obtained

[1]  Claude H. Moog,et al.  Input-output feedback linearization of time-delay systems , 2004, IEEE Transactions on Automatic Control.

[2]  Songjiao Shi,et al.  State feedback stabilization for a class of stochastic time-delay nonlinear systems , 2003, IEEE Trans. Autom. Control..

[3]  Xiaoping Liu,et al.  Comments on "Robust stabilization of a class of time-delay nonlinear systems" , 2003, IEEE Trans. Autom. Control..

[4]  Shuzhi Sam Ge,et al.  Stable adaptive control and estimation for nonlinear systems - neural and fuzzy approximator techniques: J. T. Spooner, M. Maggiore, R. Ordóñez, K. M. Passino, John Wiley & Sons, Inc., New York, 2002, ISBN: 0-471-41546-4 , 2003, Autom..

[5]  Zhong-Ping Jiang,et al.  Stable neural controller design for unknown nonlinear systems using backstepping , 2000, IEEE Trans. Neural Networks Learn. Syst..

[6]  Songjiao Shi,et al.  Output feedback stabilization for a class of stochastic time-delay nonlinear systems , 2003, IEEE Trans. Autom. Control..

[7]  Peng Shi,et al.  Robust stabilization of a class of nonlinear time-delay systems , 2004, Appl. Math. Comput..

[8]  Zhong-Ping Jiang,et al.  Small-gain theorem for ISS systems and applications , 1994, Math. Control. Signals Syst..

[9]  Martín Velasco-Villa,et al.  The disturbance decoupling problem for time-delay nonlinear systems , 2000, IEEE Trans. Autom. Control..

[10]  Shuzhi Sam Ge,et al.  Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[11]  Jie Chen,et al.  On sufficient conditions for stability independent of delay , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[12]  Changchun Hua,et al.  Comments on "State feedback stabilization for a class of stochastic time-delay nonlinear systems" , 2004, IEEE Trans. Autom. Control..

[13]  E. Boukas,et al.  DELAY-DEPENDENT STABILIZATION OF SINGULAR LINEAR SYSTEMS WITH DELAYS , 2006 .

[14]  E. Boukas,et al.  Delay-dependent stability and output feedback stabilisation of Markov jump system with time-delay , 2002 .

[15]  Magdi S. Mahmoud,et al.  Methodologies for Control of Jump Time-Delay Systems , 2003 .

[16]  Shuzhi Sam Ge,et al.  Adaptive neural control of uncertain MIMO nonlinear systems , 2004, IEEE Transactions on Neural Networks.

[17]  Eduardo Sontag,et al.  Changing supply functions in input/state stable systems , 1995, IEEE Trans. Autom. Control..

[18]  Alfredo Germani,et al.  On the existence of the linearizing state-feedback for nonlinear delay systems , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[19]  Shengyuan Xu,et al.  Robust H∞ control for a class of uncertain nonlinear two-dimensional systems with state delays , 2005, J. Frankl. Inst..

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

[21]  Vladimir L. Kharitonov,et al.  Stability of Time-Delay Systems , 2003, Control Engineering.

[22]  Changchun Hua,et al.  Robust stabilization of uncertain dynamic time-delay systems with unknown bounds of uncertainties , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[23]  Zhong-Ping Jiang,et al.  Decentralized and adaptive nonlinear tracking of large-scale systems via output feedback , 2000, IEEE Trans. Autom. Control..

[24]  Miroslav Krstic,et al.  Nonlinear and adaptive control de-sign , 1995 .

[25]  Mrdjan Jankovic,et al.  Control Lyapunov-Razumikhin functions and robust stabilization of time delay systems , 2001, IEEE Trans. Autom. Control..

[26]  Panagiotis D. Christofides,et al.  Non-linear feedback control of parabolic partial differential difference equation systems , 2000 .

[27]  Zhong-Ping Jiang,et al.  Design of Robust Adaptive Controllers for Nonlinear Systems with Dynamic Uncertainties , 1998, Autom..

[28]  Shuzhi Sam Ge,et al.  Adaptive neural network control of nonlinear systems with unknown time delays , 2003, IEEE Trans. Autom. Control..

[29]  Sing Kiong Nguang,et al.  Robust stabilization of a class of time-delay nonlinear systems , 2000, IEEE Trans. Autom. Control..

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

[31]  Jay A. Farrell,et al.  Adaptive observer backstepping control using neural networks , 2001, IEEE Trans. Neural Networks.

[32]  Kevin M. Passino,et al.  Stable Adaptive Control and Estimation for Nonlinear Systems , 2001 .

[33]  P. Shi Filtering on sampled-data systems with parametric uncertainty , 1998, IEEE Trans. Autom. Control..