Abstract
In a discrete-time framework any nonlinear system can be approximated with arbitrarily small error by a Volterra series and also by a “sandwich” system.
Similar content being viewed by others
References
Dieudonné, J.: Foundations of modern analysis. Berlin, Heidelberg, New York: Springer 1976
Hille, E., Phillips, R.S.: Functional analysis and semi-groups. Providence: AMS 1957
Kolmogoroff, A.N.: On the representation of continuous functions of several variables by superposition of continuous functions of one variable and addition (russian). Dokl. Akad. Nauk SSSR 114, 953–956 (1957); AMS Transl. 2, 55–59 (1963)
Lorentz, G.G.: Approximation of functions. New York: Holt, Rinehart, and Winston 1967
Minsky, M., Papert, S.: Perceptrons. Cambridge, Mass.: MIT 1968
Muroga, S.: Threshold logic and its applications. New York, London: Wiley and Sons 1971
Palm, G., Poggio, T.: The Volterra representation and the Wiener expansion: Validity and pitfalls. SIAM J. Appl. Math. 33, 195–216 (1977)
Palm, G., Poggio, T.: Stochastic identification methods for nonlinear systems: an extension of the Wiener theory. SIAM J. Appl. Math. 34, 524–534 (1978)
Palm, G., Poggio, T.: Discrete system theory (in preparation)
Palm, G.: On representation and approximation of nonlinear systems. Biol. Cybernetics 31, 119–124 (1978)
Sprecher, D.A.: An improvement in the superposition theorem of Kolmogorov. J. Math. Anal. Appl. 38, 208–213 (1972)
Varjú, D.: Systemtheorie. Berlin, Heidelberg, New York: Springer 1978
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Palm, G. On representation and approximation of nonlinear systems. Biol. Cybernetics 34, 49–52 (1979). https://doi.org/10.1007/BF00336857
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00336857