Adaptive control of nonlinear dynamic systems using θ-adaptive neural networks

Abstract The adaptive control of dynamic systems with nonlinear parametrization is considered. An algorithm based on a neural network, similar to the TANN algorithm proposed in Annaswamy and Yu (1996), is suggested for adjusting the control parameters. The resulting adaptive controller is shown to lead to stability of the closed-loop system. How the neural network is trained off-line in order to lead to closed-loop stability is described in detail. The resulting improvement in performance using this neural controller over other methods proposed in the literature including extended Kalman filter, linear adaptive control, and other neural strategies is demonstrated through simulation studies.

[1]  Anuradha M. Annaswamy,et al.  Mode-Based Neural Algorithms for Parameter Estimation , 1998, Inf. Sci..

[2]  R. Kanellakopoulos A discrete-time adaptive nonlinear system , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[3]  P. Parks,et al.  Liapunov redesign of model reference adaptive control systems , 1966 .

[4]  Anuradha M. Annaswamy,et al.  Θ-adaptive Neural Networks: a New Approach to Parameter Estimation , 1996, IEEE Trans. Neural Networks.

[5]  Chen-Chung Liu,et al.  Adaptively controlling nonlinear continuous-time systems using multilayer neural networks , 1994, IEEE Trans. Autom. Control..

[6]  Mahmoud M. Gabr,et al.  ON THE IDENTIFICATION OF BILINEAR SYSTEMS FROM OPERATING RECORDS , 1982 .

[7]  J. Munkres Analysis On Manifolds , 1991 .

[8]  S. Billings,et al.  Least squares parameter estimation algorithms for non-linear systems , 1984 .

[9]  K. Narendra,et al.  Stable model reference adaptive control in the presence of bounded disturbances , 1982 .

[10]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[11]  Michael I. Jordan,et al.  Forward Models: Supervised Learning with a Distal Teacher , 1992, Cogn. Sci..

[12]  K. L. Nielsen,et al.  An Algorithm for Least Squares , 1947 .

[13]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[14]  Jooyoung Park,et al.  Universal Approximation Using Radial-Basis-Function Networks , 1991, Neural Computation.

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

[16]  William A. Sethares,et al.  Nonlinear parameter estimation via the genetic algorithm , 1994, IEEE Trans. Signal Process..

[17]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

[18]  A. Annaswamy,et al.  Adaptive control of nonlinear systems with a triangular structure , 1994, IEEE Trans. Autom. Control..

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

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

[21]  H. Spang,et al.  Second-order correlation method for bilinear system identification , 1977, 1977 IEEE Conference on Decision and Control including the 16th Symposium on Adaptive Processes and A Special Symposium on Fuzzy Set Theory and Applications.

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

[23]  Kumpati S. Narendra,et al.  Control of nonlinear dynamical systems using neural networks: controllability and stabilization , 1993, IEEE Trans. Neural Networks.

[24]  T. Subba Rao,et al.  On the identification of bilinear systems from operating records , 1984 .

[25]  Andrew R. Barron,et al.  Universal approximation bounds for superpositions of a sigmoidal function , 1993, IEEE Trans. Inf. Theory.

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

[27]  Thomas Parisini,et al.  Neural networks for feedback feedforward nonlinear control systems , 1994, IEEE Trans. Neural Networks.

[28]  B. Widrow,et al.  Neural networks for self-learning control systems , 1990, IEEE Control Systems Magazine.

[29]  D. Marquardt An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[30]  L. Ljung,et al.  Recursive identification of bilinear systems , 1987 .

[31]  Gerald E. Peterson,et al.  Using neural networks for aerodynamic parameter modeling , 1995, Proceedings of 1995 American Control Conference - ACC'95.

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

[33]  Hassan K. Khalil,et al.  Adaptive control of a class of nonlinear discrete-time systems using neural networks , 1995, IEEE Trans. Autom. Control..

[34]  Richard D. Braatz,et al.  On the "Identification and control of dynamical systems using neural networks" , 1997, IEEE Trans. Neural Networks.

[35]  Nader Sadegh,et al.  A perceptron network for functional identification and control of nonlinear systems , 1993, IEEE Trans. Neural Networks.

[36]  R. Palmer,et al.  Introduction to the theory of neural computation , 1994, The advanced book program.

[37]  Antonio Moran,et al.  Optimal Active Control of Nonlinear Vehicle Suspensions Using Neural Networks , 1994 .

[38]  L. Acar,et al.  Real-time nonlinear optimal control using neural networks , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[39]  Anders Krogh,et al.  Introduction to the theory of neural computation , 1994, The advanced book program.

[40]  Liang Jin,et al.  Fast neural learning and control of discrete-time nonlinear systems , 1995, IEEE Trans. Syst. Man Cybern..

[41]  K. Narendra,et al.  Bounded error adaptive control , 1980, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[42]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1992, Math. Control. Signals Syst..

[43]  K. Narendra,et al.  Robust adaptive control in the presence of bounded disturbances , 1986 .

[44]  L. Acosta,et al.  Two approaches to nonlinear systems optimal control by using neural networks , 1994, Proceedings of 1994 IEEE International Conference on Neural Networks (ICNN'94).

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