Passivation and control of partially known SISO nonlinear systemsvia dynamic neural networks

In this paper, an adaptive technique is suggested to provide the passivity property for a class of partially known SISO nonlinear systems. A simple Dynamic Neural Network (DNN), containing only two neurons and without any hidden-layers, is used to identify the unknown nonlinear system. By means of a Lyapunov-like analysis the new learning law for this DNN, guarantying both successful identification and passivation effects, is derived. Based on this adaptive DNN model, an adaptive feedback controller, serving for wide class of nonlinear systems with an a priori incomplete model description, is designed. Two typical examples illustrate the effectiveness of the suggested approach.

[1]  M. Polycarpou,et al.  Stable adaptive tracking of uncertain systems using nonlinearly parametrized on-line approximators , 1998 .

[2]  I. Kanellakopoulos,et al.  Backstepping to passivity: recursive design of adaptive systems , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[3]  J. Willems.  Dissipative dynamical systems Part II: Linear systems with quadratic supply rates , 1972 .

[4]  F. Lewis,et al.  Guest editorial: Neural network feedback control with guaranteed stability , 1998 .

[5]  David J. Hill,et al.  Stability results for nonlinear feedback systems , 1977, Autom..

[6]  I. Kanellakopoulos.  Passive adaptive control of non‐linear systems , 1993 .

[7]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

[8]  Nader Sadegh.  A multilayer nodal link perceptron network with least squares training algorithm , 1998 .

[9]  David J. Hill,et al.  Nonlinear adaptive control of feedback passive systems , 1995, Autom..

[10]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[11]  Alexander S. Poznyak,et al.  Stability analysis of dynamic neural control , 1998 .

[12]  A. Poznyak,et al.  Passivity feedback equivalence of nonlinear systems via neural networks approximation , 1999, 1999 European Control Conference (ECC).

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

[14]  J. Willems.  Dissipative dynamical systems part I: General theory , 1972 .

[15]  Lihua Xie,et al.  Robust control of nonlinear feedback passive systems , 1996 .

[16]  A. Isidori,et al.  Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems , 1991 .