Identification and suboptimal control of heat exchanger using generalized back propagation through time

• Autorzy: Fujarewicz K.
• Języki publikacji: EN

Abstrakty

EN

This paper deals with a problem of identification and suboptimal control of a counterflow heat exchanger. From the point of view of control theory the heat exchanger is a nonlinear, multidimensional, distributed parameter, dynamical system, and due to its complexity it is difficult to identify it as a black box. In this paper a hybrid model containing neural networks is identified. Its complicated structure makes the analytical calculation of the gradient of performance index with respect to neural network weights very difficult. This problem is solved using a special, structural formulation of sensitivity analysis called generalized back propagation through time (GBPTT). This method is universal, can be used for searching suboptimal parameters (weights) or suboptimal control signals in continuous or discrete time, nonlinear, dynamical systems. Moreover, the presented method is fully mnemonic. The obtained model of the heat exchanger and the same methodology is used during the gradient calculation of the suboptimal control signal of the heat exchanger. Numerical examples are presented.

Słowa kluczowe

EN

identification; nonlinear systems; distributed-parameter systems; artificial neural network

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2000
• Tom: Vol. 10, no. 3/4
• Strony: 167--183
• Opis fizyczny: Bibliogr. 15 poz., rys., tab., wzory

Twórcy

autor

Fujarewicz K.

• Institute of Automatic Control, Silesian University of Technology, Gliwice, Poland

Bibliografia

• [1] M. S. Ahmed: Block partial derivative and its application to neural net-based direct-model-reference adaptive control. IEE Proc.-Control Theory Appl., 141 (1994), 305-314.
• [2] P. Baldi: Gradient descent learning algorithm overview: A general dynamical systems perspective. IEEE Trans, Neural Networks, 6 (1995), 182-195.
• [3] J. B. Cruz (Ed.): System sensitivity analysis. Benchmark papers in electrical engineering and computer science. Dowden. Hutchinson & Ross, Inc., Stroudsburg, 1973.
• [4] K. Fujarewicz: Optimal control of nonlinear systems using generalized back propagation through time. Proc. Eighteenth I AST ED Conference Modelling, Identification and Control, Innsbruck, Austria, 1999.
• [5] K. Fujarewicz: Systems transposed in lime and their application to gradient calculation in dynamical systems containing neural nets. Proc. Fourth Conference - Neural Networks and Their Applications, Zakopane, Poland, 1999.
• [6] K. Fujarewicz: Control of certain nonlinear systems using neural networks. Ph.D. thesis, Silesian Technical University, 1999.
• [7] T. Kailath: Linear Systems. Prentice-Hall, Inc., Engelwood Cliffs, N.J., 1980.
• [8] P. Laszczyk and M. Metzger: Application of hybrid ANN/Physical model for simulation of distributed parameter heat exchangers. Proc. 10th European Simulation Symposium, Nottingham, United Kingdom, 1998.
• [9] S. N. Narendra and K. Parthasarathy: Gradient methods for the optimization of dynamical systems containing neural networks. IEEE Trans. Neural Networks, 2 (1991), 252-262.
• [10] B. A. Pearlmutter: Gradient calculations for dynamic recurrent neural networks: A survey. IEEE Trans. Neural Networks, 6 (1995), 1212-1228.
• [11] Y. Takahashi: Transfer function analysis of heat exchange process. In A. Tustin (Ed.): Automatic A Manual Control, (1952), 235-247.
• [12] E. Wan and F. Beaufays: Diagrammatic derivation of gradient algorithms for neural networks. Neural Computation, 8(1), (1996), 182-201.
• [13] P. J. Werbos: Backpropagation through time: what it does and how to do it. Proc. IEEE. 78 (1990). 1550-1560.
• [14] A. Wierzbicki: Models and sensitivity of control systems. WNT, Warsaw, 1977.
• [15] R. Williams and D. Zipser: Learning algorithm for continually running fully recurrent neural networks. Neural Computation, 1 (1989), 270-280.