Robust backstepping control of robotic systems using neural networks

Neural network (NN) controllers for the robust backstepping control of robotic systems in both continuous and discrete-time are presented. Control input is selected to achieve tracking performance for unknown nonlinear systems. Tuning methods are derived for the NN based on the delta rule. Novel weight tuning algorithms for the NN are obtained that are similar to /spl epsiv/-modification in the case of continuous-time adaptive control. Uniform ultimate boundedness of the tracking error and the weight estimates are presented without using the persistency of excitation (PE) condition. Certainty equivalence is not used and a regression matrix is not computed. No learning phase is needed for the NN and initialization of the network weights is straightforward.

[1]  Anuradha M. Annaswamy,et al.  Stable Adaptive Systems , 1989 .

[2]  I. Kanellakopoulos.  A discrete-time adaptive nonlinear system , 1994, IEEE Trans. Autom. Control..

[3]  Lennart Ljung,et al.  Theory and Practice of Recursive Identification , 1983 .

[4]  Frank L. Lewis,et al.  Discrete-time neural net controller with guaranteed performance , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[5]  Ioan D. Landau.  Evolution of Adaptive Control , 1993 .

[6]  Karl Johan Åström,et al.  Adaptive Control , 1989, Embedded Digital Control with Microcontrollers.

[7]  Frank L. Lewis,et al.  Robust implicit self-tuning regulator: Convergence and stability , 1996, Autom..

[8]  Frank L. Lewis,et al.  Control of Robot Manipulators , 1993 .

[9]  P.V. Kokotovic,et al.  The joy of feedback: nonlinear and adaptive , 1992, IEEE Control Systems.

[10]  Frank L. Lewis,et al.  Multilayer discrete-time neural-net controller with guaranteed performance , 1996, IEEE Trans. Neural Networks.

[11]  Frank L. Lewis,et al.  CMAC neural network control of robot manipulators , 1997 .

[12]  H. Khalil,et al.  Adaptive control of a class of nonlinear systems using neural networks , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[13]  Frank L. Lewis,et al.  Neural net robot controller with guaranteed tracking performance , 1995, IEEE Trans. Neural Networks.

[14]  Robert M. Sanner,et al.  Gaussian Networks for Direct Adaptive Control , 1991, 1991 American Control Conference.

[15]  Kumpati S. Narendra,et al.  Identification and control of dynamical systems using neural networks , 1990, IEEE Trans. Neural Networks.

[16]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[17]  Graham C. Goodwin,et al.  Adaptive filtering prediction and control , 1984 .

[18]  Kouhei Ohnishi,et al.  Sliding modes in power converters and motion control systems , 1993 .

[19]  K. Narendra,et al.  A new adaptive law for robust adaptation without persistent excitation , 1987 .

[20]  Y. D. Landau,et al.  Adaptive control: The model reference approach , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[21]  Sarangapani Jagannathan.  Adaptive control of unknown feedback linearizable systems in discrete-time using neural networks , 1996, Proceedings of IEEE International Conference on Robotics and Automation.