Frequency analysis of nonlinear dynamical systems and the control of vibration

• Autorzy: Banks S. P. , Tomas-Rodriguez M.
• Języki publikacji: EN

Abstrakty

EN

In this paper we shall consider nonlinear vibrating systems which can be written in form x= A(x)+B(x)u. We shall introduce a sequence of linear, time-varying approximations which can be studied in the frequency domain. A spectral optimal control theory will be developed.

Słowa kluczowe

EN

nonlinear vibrating systems; approximation theory; optimal control

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2003
• Tom: Vol. 13, no. 3
• Strony: 269--279
• Opis fizyczny: Bibliogr. 23 poz, wzory

Twórcy

autor

Banks S. P.

• Department of Automatic Control and Systrms Engineering, University of Sheffield, UK

autor

Tomas-Rodriguez M.

• Department of Automatic Control and Systrms Engineering, University of Sheffield, UK

Bibliografia

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• [17] D. McCaffrey and S.P. Banks: Lagrangian manifolds, viscosity solutions and Maslov index. J. Convex Anal., 9 (2002), 185-224.
• [18] D. McCaffrey And S.P. Banks: Lagrangian manifolds and nonlinear optimal regulators. Invited presentation for ICOTA conf. on optimisation theory, Hong Kong, (2001).
• [19] D. Salamon: Morse Theory, the Conley Index and Floer Homology. Bull. LMS, 22 (1990), 113-140.
• [20] D. Salamon: Connected simple systems and the Conley index of isolated invariant sets. Trans. Amer. Math. Soc., 291 (1985), 1-41.
• [21] S. Smale: Differentiable dynamical systems. Bull. Am. Math. Soc., 73 (1967), 747-817.
• [22] M. Tomas-Rodriguez and S.P. Banks: Linear Approximations to Nonlinear Dynamical Systems with Applications to Stability and Spectral Theory. IMA J. Math. Cont. & Inf., 20 (2003), 89-104.
• [23] S. Wiggins: Global Bifurcations and Chaos. App. Math. Sci., 73 Springer-Verlag, New York, 1988.