A new control method of nonlinear systems based on impulse responses of universal learning networks

A new control method of nonlinear dynamic systems is proposed based on the impulse responses of universal learning networks (ULNs), ULNs form a superset of neural networks. They consist of a number of interconnected nodes where the nodes may have any continuously differentiable nonlinear functions in them and each pair of nodes can be connected by multiple branches with arbitrary time delays. A generalized learning algorithm is derived for the ULNs, in which both the first order derivatives (gradients) and the higher order derivatives are incorporated. One of the distinguished features of the proposed control method is that the impulse response of the systems is considered as an extended part of the criterion function and it can be calculated by using the higher order derivatives of ULNs. By using the impulse response as the criterion function, nonlinear dynamics with not only quick response but also quick damping and small steady state error can be more easily obtained than the conventional nonlinear control systems with quadratic form criterion functions of state and control variables.

[1]  Kotaro Hirasawa,et al.  Universal learning network and its application to chaos control , 2000, Neural Networks.

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

[3]  P. Werbos,et al.  Beyond Regression : "New Tools for Prediction and Analysis in the Behavioral Sciences , 1974 .

[4]  Ronald J. Williams,et al.  A Learning Algorithm for Continually Running Fully Recurrent Neural Networks , 1989, Neural Computation.

[5]  W. Wonham.  On pole assignment in multi-input controllable linear systems , 1967 .

[6]  Kumpati S. Narendra,et al.  Gradient methods for the optimization of dynamical systems containing neural networks , 1991, IEEE Trans. Neural Networks.

[7]  John Moody,et al.  Fast Learning in Networks of Locally-Tuned Processing Units , 1989, Neural Computation.

[8]  Chin-Teng Lin,et al.  A second-order learning algorithm for multilayer networks based on block Hessian matrix , 1998, Neural Networks.

[9]  John J. Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities , 1999 .

[10]  K. S. Narendra,et al.  Neural networks for control theory and practice , 1996, Proc. IEEE.

[11]  Wray L. Buntine,et al.  Computing second derivatives in feed-forward networks: a review , 1994, IEEE Trans. Neural Networks.

[12]  Arthur E. Bryson,et al.  Applied Optimal Control , 1969 .

[13]  Kotaro Hirasawa,et al.  Forward propagation universal learning network , 1996, Proceedings of International Conference on Neural Networks (ICNN'96).

[14]  Huibert Kwakernaak,et al.  Linear Optimal Control Systems , 1972 .

[15]  Kotaro Hirasawa,et al.  Universal learning network and computation of its higher order derivatives , 1995, Proceedings of ICNN'95 - International Conference on Neural Networks.

[16]  Kotaro Hirasawa,et al.  Modeling dynamic systems using universal learning network , 1996, 1996 IEEE International Conference on Systems, Man and Cybernetics. Information Intelligence and Systems (Cat. No.96CH35929).

[17]  W. Pitts,et al.  A Logical Calculus of the Ideas Immanent in Nervous Activity (1943) , 2021, Ideas That Created the Future.

[18]  F ROSENBLATT,et al.  The perceptron: a probabilistic model for information storage and organization in the brain. , 1958, Psychological review.

[19]  Judith E. Dayhoff,et al.  Trajectory production with the adaptive time-delay neural network , 1995, Neural Networks.

[20]  K S Narendra,et al.  Control of nonlinear dynamical systems using neural networks. II. Observability, identification, and control , 1996, IEEE Trans. Neural Networks.

[21]  Kotaro Hirasawa,et al.  Universal learning network and its application to robust control , 2000, IEEE Trans. Syst. Man Cybern. Part B.

[22]  K S Narendra,et al.  IDENTIFICATION AND CONTROL OF DYNAMIC SYSTEMS USING NEURAL NETWORKS , 1990 .

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