Further Results on the Use of Nussbaum Gains in Adaptive Neural Network Control

In this note, the use of Nussbaum gains for adaptive neural network (NN) control is examined. Extending previous approaches that have been successfully applied to prove the forward completeness property (boundedness up to finite time), we address the boundedness for all time (up to infinity) problem. An example is constructed showing that this is not possible in general with the existing theoretical tools. To achieve boundedness for all time, a novel hysteresis-based deadzone scheme with resetting is introduced for the associated update laws. In this way, a unique, piecewise continuously differentiable solution is obtained while the error converges in finite time within some arbitrarily small region of the origin. Using the proposed modification, an adaptive NN tracking controller is designed for a class of multiple-input multiple-output nonlinear systems.

[1]  B. Paden,et al.  Lyapunov stability theory of nonsmooth systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[2]  Shuzhi Sam Ge,et al.  Adaptive Neural Network Tracking Control of MIMO Nonlinear Systems With Unknown Dead Zones and Control Directions , 2009, IEEE Transactions on Neural Networks.

[3]  Tao Zhang,et al.  Stable adaptive control for nonlinear multivariable systems with a triangular control structure , 2000, IEEE Trans. Autom. Control..

[4]  X. Ye,et al.  Adaptive nonlinear design without a priori knowledge of control directions , 1998, IEEE Trans. Autom. Control..

[5]  Pingjing Yao,et al.  Adaptive neural network control for a class of low-triangular-structured nonlinear systems , 2006, IEEE Transactions on Neural Networks.

[6]  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..

[7]  J. Cortés.  Discontinuous dynamical systems , 2008, IEEE Control Systems.

[8]  Shuzhi Sam Ge,et al.  Robust adaptive neural control for a class of perturbed strict feedback nonlinear systems , 2002, Proceedings of the 4th World Congress on Intelligent Control and Automation (Cat. No.02EX527).

[9]  Eugene P. Ryan,et al.  Universal λ-tracking for nonlinearly-perturbed systems in the presence of noise , 1994, Autom..

[10]  E. Ryan.  A nonlinear universal servomechanism , 1994, IEEE Trans. Autom. Control..

[11]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[12]  A. Morse,et al.  Applications of hysteresis switching in parameter adaptive control , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

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

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

[15]  F. Hong,et al.  Robust adaptive control for a class of uncertain strict‐feedback nonlinear systems , 2009 .

[16]  Eric Rogers,et al.  Uncertainty, performance, and model dependency in approximate adaptive nonlinear control , 2000, IEEE Trans. Autom. Control..

[17]  Marios M. Polycarpou,et al.  High-order neural network structures for identification of dynamical systems , 1995, IEEE Trans. Neural Networks.

[18]  M. Polycarpou,et al.  On the existence and uniqueness of solutions in adaptive control systems , 1993, IEEE Trans. Autom. Control..

[19]  Elias B. Kosmatopoulos,et al.  A switching adaptive controller for feedback linearizable systems , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[20]  G. Goodwin,et al.  Hysteresis switching adaptive control of linear multivariable systems , 1994, IEEE Trans. Autom. Control..

[21]  Xin-Ping Guan,et al.  Adaptive Fuzzy Output-Feedback Controller Design for Nonlinear Time-Delay Systems With Unknown Control Direction , 2009, IEEE Trans. Syst. Man Cybern. Part B.

[22]  Haris E. Psillakis.  Projection-Based Adaptive Neurocontrol With Switching Logic Deadzone Tuning , 2009, IEEE Transactions on Neural Networks.

[23]  R. Nussbaum.  Some remarks on a conjecture in parameter adaptive control , 1983 .