A new framework of learning control for a class of nonlinear systems

This paper illustrates a new nonlinear learning control design based on Lyapunov's direct method. The design is applicable to the class of nonlinear systems consisting of finite cascaded subsystems in performing repeated tasks. A class of difference or difference-differential learning laws is proposed. It is shown that, under a difference learning control, the class of nonlinear systems is guaranteed to be asymptotically stable with respect to the number of trials. For better rejection of measurement noise, the difference-differential learning law can be applied to yield arbitrarily good accuracy. The proposed approach provides closed-form expressions of learning controls, and it gives the designer much flexibility in choosing various combinations of feedforward and learning control parts.

[1]  B. Paden,et al.  Stability of learning control with disturbances and uncertain initial conditions , 1992 .

[2]  Darren M. Dawson,et al.  Linear learning control of robot motion , 1993, J. Field Robotics.

[3]  Toshiharu Sugie,et al.  An iterative learning control law for dynamical systems , 1991, Autom..

[4]  Masayoshi Tomizuka,et al.  Learning hybrid force and position control of robot manipulators , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[5]  F. Miyazaki,et al.  Bettering operation of dynamic systems by learning: A new control theory for servomechanism or mechatronics systems , 1984, The 23rd IEEE Conference on Decision and Control.

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

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

[8]  Jin Soo Lee,et al.  An iterative learning control theory for a class of nonlinear dynamic systems , 1992, Autom..

[9]  F. Miyazaki,et al.  Applications of learning method for dynamic control of robot manipulators , 1985, 1985 24th IEEE Conference on Decision and Control.

[10]  I. Kanellakopoulos,et al.  Systematic Design of Adaptive Controllers for Feedback Linearizable Systems , 1991, 1991 American Control Conference.

[11]  Luca Maria Gambardella,et al.  On the iterative learning control theory for robotic manipulators , 1988, IEEE J. Robotics Autom..

[12]  Masayoshi Tomizuka,et al.  Learning hybrid force and position control of robot manipulators , 1993, IEEE Trans. Robotics Autom..

[13]  Filson H. Glanz,et al.  Application of a General Learning Algorithm to the Control of Robotic Manipulators , 1987 .

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

[15]  Zhihua Qu,et al.  Robust Control of Nonlinear Uncertain Systems Under Generalized Matching Conditions , 1993, 1993 American Control Conference.

[16]  John B. Moore,et al.  Exponential convergence of a learning controller for robot manipulators , 1991 .

[17]  John Hauser,et al.  Learning control for a class of nonlinear systems , 1987, 26th IEEE Conference on Decision and Control.

[18]  S. Arimoto,et al.  Learning control theory for dynamical systems , 1985, 1985 24th IEEE Conference on Decision and Control.