Adaptive Repetitive Control for a Class of Nonlinearly Parametrized Systems

In this note, Lyapunov-based adaptive repetitive control is presented for a class of nonlinearly parametrized systems. Through the use of an integral Lyapunov function, the controller singularity problem is elegantly solved as it avoids the nonlinear parametrization from entering into the adaptive control and repetitive control. Global stability of the adaptive system and asymptotic convergence of the tracking error are established, and tracking error bounds are provided to quantify the control performance. Both partially and fully saturated learning laws are analyzed in detail, and compared analytically

[1]  J. Y. Choi,et al.  Adaptive iterative learning control of uncertain robotic systems , 2000 .

[2]  Tae-Yong Kuc,et al.  An adaptive PID learning control of robot manipulators , 2000, Autom..

[3]  J. S. Lee,et al.  An adaptive learning control of uncertain robotic systems , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

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

[5]  Z. Qu,et al.  Non-linear learning control of robot manipulators without requiring acceleration measurement , 1993 .

[6]  R. Marino,et al.  Global adaptive output-feedback control of nonlinear systems , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[7]  Tong Heng Lee,et al.  Iterative learning control design based on composite energy function with input saturation , 2004, Autom..

[8]  Dimitry Gorinevsky,et al.  Distributed Loop-shaping for Iterative Control of Batch Processes , 2002 .

[9]  S. Ge,et al.  Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[10]  Roberto Horowitz,et al.  A new adaptive learning rule , 1991 .

[11]  Suguru Arimoto,et al.  Learning control theory for robotic motion , 1990 .

[12]  Tao Zhang,et al.  Stable Adaptive Neural Network Control , 2001, The Springer International Series on Asian Studies in Computer and Information Science.

[13]  Carlos Canudas de Wit,et al.  A survey of models, analysis tools and compensation methods for the control of machines with friction , 1994, Autom..

[14]  Tae-Yong Kuc,et al.  Adaptive learning control of uncertain robotic systems , 1996 .

[15]  Ying Tan,et al.  Iterative learning control design based on composite energy function with input saturation , 2003, Proceedings of the 2003 American Control Conference, 2003..

[16]  Li Xu,et al.  Adaptive robust repetitive control of a class of nonlinear systems in normal form with applications to motion control of linear motors , 2001, 2001 IEEE/ASME International Conference on Advanced Intelligent Mechatronics. Proceedings (Cat. No.01TH8556).

[17]  J. Boskovic.  Stable adaptive control of a class of first-order nonlinearly parameterized plants , 1995, IEEE Trans. Autom. Control..

[18]  Z. Qu,et al.  Model‐Based Learning Controls And Their Comparisons Using Lyapunov Direct Method , 2002 .

[19]  Anuradha M. Annaswamy,et al.  Adaptive control of continuous time systems with convex/concave parametrization , 1998, Autom..

[20]  Zhihua Qu.  Adaptive and robust controls of uncertain systems with nonlinear parameterization , 2003, IEEE Trans. Autom. Control..

[21]  Warren E. Dixon,et al.  Repetitive learning control: a Lyapunov-based approach , 2002, IEEE Trans. Syst. Man Cybern. Part B.

[22]  Masayoshi Tomizuka,et al.  Analysis and Synthesis of Discrete-Time Repetitive Controllers , 1989 .

[23]  Tsu-Chin Tsao,et al.  Repetitive learning of backstepping controlled nonlinear electrohydraulic material testing system , 2002 .

[24]  S. Hara,et al.  Repetitive control system: a new type servo system for periodic exogenous signals , 1988 .

[25]  Masayoshi Tomizuka,et al.  A unified approach to the design of adaptive and repetitive controllers for robotic manipulators , 1990 .

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

[27]  Mingxuan Sun,et al.  Adaptive rejection of periodic & non-periodic disturbances for a class of nonlinearly parametrized systems , 2004, Proceedings of the 2004 American Control Conference.