Adaptive learning control for nonlinear systems with extended matching unstructured uncertainties

The output tracking control problem via state feedback is addressed for a class of single input-single output nonlinear systems which are affected by extended matching unstructured uncertainties. Under the assumption that the output reference signal is sufficiently smooth and periodic with known period, a robust adaptive learning control is designed, which learns the unstructured unknown periodic disturbance signals due to system uncertainties by identifying the Fourier coefficients of any truncated approximation while guaranteeing L2 and L¿ transient performances. For any initial condition of the system in an arbitrary given compact set, by properly setting the control parameters: i) the output tracking error exponentially converges to a residual set which may be arbitrarily reduced by increasing the number of terms in the truncated Fourier series expansions; ii) when the unknown periodic disturbances can be represented by finite Fourier series expansions, the output tracking error exponentially converges to zero.

[1]  Bin Yao,et al.  Neural network adaptive robust control of nonlinear systems in semi-strict feedback form , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[2]  Masayoshi Tomizuka,et al.  Adaptive robust control of SISO nonlinear systems in a semi-strict feedback form , 1997, Autom..

[3]  M. French,et al.  Non-linear iterative learning by an adaptive Lyapunov technique , 2000 .

[4]  Chiang-Ju Chien,et al.  A Unified Adaptive Iterative Learning Control Framework for Uncertain Nonlinear Systems , 2007, IEEE Transactions on Automatic Control.

[5]  Tamer Basar,et al.  Disturbance attenuating controller design for strict-feedback systems with structurally unknown dynamics , 2001, Autom..

[6]  Jian-Xin Xu,et al.  A new periodic adaptive control approach for time-varying parameters with known periodicity , 2004, IEEE Transactions on Automatic Control.

[7]  Wen-Jun Cao,et al.  On Functional Approximation of the Equivalent Control Using Learning Variable Structure Control , 2000 .

[8]  Ying Tan,et al.  A composite energy function-based learning control approach for nonlinear systems with time-varying parametric uncertainties , 2002, IEEE Trans. Autom. Control..

[9]  V. O. Nikiforov,et al.  Nonlinear servocompensation of unknown external disturbances , 2001, Autom..

[10]  R. Marino,et al.  Global Iterative Learning Control Of Feedback Linearizable Systems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[11]  Masayoshi Tomizuka,et al.  Adaptive robust control of MIMO nonlinear systems in semi-strict feedback forms , 2001, Autom..

[12]  Mingxuan Sun,et al.  Iterative learning control with initial rectifying action , 2002, Autom..

[13]  N. G. Parke,et al.  Ordinary Differential Equations. , 1958 .

[14]  I.G. Polushin,et al.  Cascaded Iterative Learning Control for a Class of Uncertain Time-Varying Nonlinear Systems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[15]  Wei Wang,et al.  On Learning Wavelet Control for Affine Nonlinear Systems , 2007, 2007 American Control Conference.

[16]  Domitilla Del Vecchio,et al.  Adaptive Learning Control for Feedback Linearizable Systems , 2003, Eur. J. Control.

[17]  P. Tomei,et al.  Adaptive tracking for a class of feedback linearizable systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[18]  Jian-Xin Xu,et al.  Observer based learning control for a class of nonlinear systems with time-varying parametric uncertainties , 2004, IEEE Transactions on Automatic Control.

[19]  Zhihua Qu,et al.  Nonlinear learning control for a class of nonlinear systems , 2001, Autom..

[20]  Yu-Ping Tian,et al.  Robust learning control for a class of nonlinear systems with periodic and aperiodic uncertainties , 2003, Autom..

[21]  Zhihua Qu,et al.  Asymptotic learning control for a class of cascaded nonlinear uncertain systems , 2002, IEEE Trans. Autom. Control..

[22]  D. Lieberman,et al.  Fourier analysis , 2004, Journal of cataract and refractive surgery.

[23]  L. Praly,et al.  Adaptive nonlinear regulation: estimation from the Lyapunov equation , 1992 .

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

[25]  Warren E. Dixon,et al.  Comments on "A composite energy function-based learning control approach for nonlinear systems with time-varying parametric uncertainties" , 2003, IEEE Trans. Autom. Control..

[26]  Cong Wang,et al.  Learning from neural control , 2006, IEEE Transactions on Neural Networks.

[27]  V. Arnold,et al.  Ordinary Differential Equations , 1973 .

[28]  Chia-Yu Yao,et al.  Iterative learning of model reference adaptive controller for uncertain nonlinear systems with only output measurement , 2004, Autom..

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