Abstract
A novel neural net-based approach for H ∞ control design of a class of nonlinear continuous-time systems is presented. In the proposed frameworks, the nonlinear system models are approximated by multilayer neural networks. The neural networks are piecewisely interpolated to generate a linear differential inclusion models by which a linear state feedback H ∞ control law can be constructed. It is shown that finding the permissible control gain matrices can be transformed to a standard linear matrix inequality problem and solved using the available computer software.
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Basar, T. and Benhard, P.: H1-optimal control and related minimax problems, Birkhauser, Berlin, 1990.
Boyd, S., Ghaoui, L. E., Feron, E. and Balakrishnan, V.: Linear matrix inequalities in system and control theory, SIAM, Philadelphia, 1994.
Chen, B. S., Lee, T. S. and Feng, J. H.: A nonlinear control H1 design in roboticsyst ems under parameter perturbation and external disturbance, Int. J. Control 59 (1994), 439–461.
Chen, F. C. and Liu, C. C.: Adaptively controlling nonlinear continuous-time systems using multilayer neural networks, IEEE Trans. Automat. Contr. 39 (1994), 1306–1310.
Funahashi, K. I.: On the approximate realization of continuous Mappings by neural networks, Neural Networks 2 (1989), 183–192.
Horn, R. A. and Johnson, C. R.: Matrix analysis, Cambridge Univ. Press., Cambridge, U.K., 1985.
Limanond, S. and Si, J.: Neural-network-based control design: an LMI approach, IEEE Trans. Neural Networks 9 (1998), 1442–1429.
Ma, X. J., Sun, Z. Q. and He, Y. Y.: Analysis and design of fuzzy controller and fuzzy observer, IEEE Trans. Fuzzy Systems 6 (1998), 41–51.
Poznyak, A. S., Yu, W., Sanchez, E. N. and Perez, J. P.: Stability analysis of dynamic neural control, Expert Syst. Appl. 14 (1998), 227–236.
Sadegh, N.: A perceptron network for functional identification and control of nonlinear systems, IEEE Trans. Neural Networks 4 (1993), 982–988.
Stoorvogel, A.: The H1 control problem: a state space approach, Prentice-Hall, New York, 1992.
Suykens, J. A. K., Vandewalle, J. and De Moor, B.: Artificial neural networks for modeling and control of non-linear systems, Kluwer, Boston, MA, 1996.
Suykens, J. A. K., Vandewalle, J. and De Moor, B.: Lur'e systems with multilayer perceptron and recurrent neural networks: absolute stability and dissipativity, IEEE Trans. Automat. Contr. 44 (1999), 770–774.
Tanaka, K.: An approach to stability criteria of neural-network control systems, IEEE Trans. Neural Networks 7 (1996), 629–642.
Wang, K. and Michel, A. N.: Robustness and perturbation analysis of a class of nonlinear systems with applications to neural networks, IEEE Trans. Circuits Syst. 41 (1994), 24–32.
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Lin, CL., Lin, TY. Neural Net-Based H ∞ Control for a Class of Nonlinear Systems. Neural Processing Letters 15, 157–177 (2002). https://doi.org/10.1023/A:1015297019806
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DOI: https://doi.org/10.1023/A:1015297019806