Dynamic neural network-based robust observers for uncertain nonlinear systems

A dynamic neural network (DNN) based robust observer for uncertain nonlinear systems is developed. The observer structure consists of a DNN to estimate the system dynamics on-line, a dynamic filter to estimate the unmeasurable state and a sliding mode feedback term to account for modeling errors and exogenous disturbances. The observed states are proven to asymptotically converge to the system states of high-order uncertain nonlinear systems through Lyapunov-based analysis. Simulations and experiments on a two-link robot manipulator are performed to show the effectiveness of the proposed method in comparison to several other state estimation methods.

[1]  Jin Young Choi,et al.  Adaptive observer for a class of nonlinear systems using neural networks , 1999, Proceedings of the 1999 IEEE International Symposium on Intelligent Control Intelligent Systems and Semiotics (Cat. No.99CH37014).

[2]  R. Ortega,et al.  A globally exponentially convergent immersion and invariance speed observer for mechanical systems with non-holonomic constraints , 2010, Autom..

[3]  Hassan K. Khalil,et al.  Error bounds in differentiation of noisy signals by high-gain observers , 2008, Syst. Control. Lett..

[4]  G. Smirnov.  Introduction to the Theory of Differential Inclusions , 2002 .

[5]  Warren E. Dixon,et al.  LaSalle-Yoshizawa Corollaries for Nonsmooth Systems , 2013, IEEE Transactions on Automatic Control.

[6]  Shankar Sastry,et al.  A calculus for computing Filippov's differential inclusion with application to the variable structure control of robot manipulators , 1986, 1986 25th IEEE Conference on Decision and Control.

[7]  Warren E. Dixon,et al.  Nonlinear Control of Engineering Systems: A Lyapunov-Based Approach , 2003 .

[8]  J. Slotine,et al.  On Sliding Observers for Nonlinear Systems , 1986, 1986 American Control Conference.

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

[10]  Shouchuan Hu.  Differential equations with discontinuous right-hand sides☆ , 1991 .

[11]  Zdzisław Denkowski,et al.  Set-Valued Analysis , 2021 .

[12]  Anthony J. Calise,et al.  Adaptive output feedback control of nonlinear systems using neural networks , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[13]  Carlos Canudas de Wit,et al.  Sliding observers for robot manipulators , 1991, Autom..

[14]  Hassan K. Khalil,et al.  Adaptive output feedback control of robot manipulators using high-gain observer , 1997 .

[15]  Yuichi Nakamura,et al.  Approximation of dynamical systems by continuous time recurrent neural networks , 1993, Neural Networks.

[16]  Jean-Jacques E. Slotine,et al.  On Sliding Observers for Nonlinear Systems , 1986 .

[17]  J. A. Ruiz Vargas,et al.  Adaptive observers for unknown general nonlinear systems , 2001, IEEE Trans. Syst. Man Cybern. Part B.

[18]  J. Park,et al.  Adaptive fuzzy observer with minimal dynamic order for uncertain nonlinear systems , 2003 .

[19]  Abdesselem Boulkroune,et al.  How to design a fuzzy adaptive controller based on observers for uncertain affine nonlinear systems , 2008, Fuzzy Sets Syst..

[20]  Darren M. Dawson,et al.  A discontinuous output feedback controller and velocity observer for nonlinear mechanical systems , 2004, Autom..

[21]  Belghith Safya,et al.  Sliding mode observer for nonlinear mechanical systems subject to nonsmooth impacts , 2010, 2010 7th International Multi- Conference on Systems, Signals and Devices.

[22]  F. Clarke.  Optimization And Nonsmooth Analysis , 1983 .

[23]  Carlos Canudas de Wit,et al.  Sliding Observers for Robot Manipulators , 1989 .

[24]  Frank L. Lewis,et al.  A dynamic recurrent neural-network-based adaptive observer for a class of nonlinear systems , 1997, Autom..

[25]  Frank L. Lewis,et al.  Neural network output feedback control of robot manipulators , 1999, IEEE Trans. Robotics Autom..

[26]  E. S. Shin,et al.  Robust output feedback control of robot manipulators using high-gain observer , 1999, Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328).

[27]  Mehrzad Namvar,et al.  Global adaptive estimation of joint velocities in robotic manipulators , 2010 .

[28]  Frank L. Lewis,et al.  Neuro-Fuzzy Control of Industrial Systems with Actuator Nonlinearities , 1987 .

[29]  D. Dawson,et al.  On the state observation and output feedback problems for nonlinear uncertain dynamic systems , 1992, Proceedings IEEE Southeastcon '92.

[30]  S. Sastry,et al.  A calculus for computing Filippov's differential inclusion with application to the variable structure control of robot manipulators , 1987 .

[31]  Dipak M. Adhyaru,et al.  State observer design for nonlinear systems using neural network , 2012, Appl. Soft Comput..

[32]  Warren E. Dixon,et al.  Robust Identification-Based State Derivative Estimation for Nonlinear Systems , 2013, IEEE Transactions on Automatic Control.

[33]  D. Signorini,et al.  Neural networks , 1995, The Lancet.

[34]  Warren E. Dixon,et al.  Dynamic neural network-based robust observers for second-order uncertain nonlinear systems , 2011, IEEE Conference on Decision and Control and European Control Conference.

[35]  Kurt Hornik,et al.  Approximation capabilities of multilayer feedforward networks , 1991, Neural Networks.

[36]  D. Mayne.  Nonlinear and Adaptive Control Design [Book Review] , 1996, IEEE Transactions on Automatic Control.

[37]  Yi Xiong,et al.  Sliding mode observer for nonlinear uncertain systems , 2001, IEEE Trans. Autom. Control..

[38]  Leonid M. Fridman,et al.  Second-order sliding-mode observer for mechanical systems , 2005, IEEE Transactions on Automatic Control.

[39]  Warren E. Dixon,et al.  Dynamic neural network-based robust identification and control of a class of nonlinear systems , 2010, 49th IEEE Conference on Decision and Control (CDC).

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