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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
Czasopismo
Rocznik
Tom
Strony
269--279
Opis fizyczny
Bibliogr. 23 poz, wzory
Twórcy
autor
- Department of Automatic Control and Systrms Engineering, University of Sheffield, UK
autor
- Department of Automatic Control and Systrms Engineering, University of Sheffield, UK
Bibliografia
- [1] S.P. Banks: Exact boundary controllability and optimal control for a generalized Korteweg-de Vries equation. J. Nonlinear Anal. - Apps and Methods, 47 (2001), 5537-5546.
- [2] S.P. Banks: Three-dimensional stratifications, knots and bifurcations of twodimensional dynamical systems. Int. J. Bifurcation & Chaos, 12(1), (2002), 1-21.
- [3] S.P. Banks: Nonlinear delay systems, Lie algebras and Lyapunov transformations. IMA J. Math. Cont & Inf., 19 (2002), 59-72.
- [4] S.P. Banks and K. Dinesh: Approximate Optimal Control and Stability of Nonlinear Finite and Infinite-Dimensional Systems. Ann. Op. Res., 98 (2000), 19-44.
- [5] S.P. Banks and T. Cimen: Approximations to characteristics of the HJB equation and viscosity solutions. Invited presentation for ICOTA conf. on optimisation theory, Hong Kong, (2001).
- [6] S.P. Banks: Viscosity solutions and approximations to characteristics of the HJB equation. Invited presentation for ICCC 2002 conf., Malenovice, Czech Rep., (2002).
- [7] S.P. Banks and P. Borruel: Systemes a retard et stabilite. Invited presentation for CIFA 2002 conf., Nantes, France, (2002), (in French).
- [8] S.P. Banks: Mathematical Theories of Nonlinear Systems. Prentice-Hall, 1988.
- [9] S.P. Banks: Signal Processing, Image Processing and Pattern Recognition. Prentice-Hall, 1990.
- [10] C.C. Conley and E. Zehnder: The Birkhoff-Lewis fixed point theorem and a conjecture of V.I. Arnold. Inv. Math., 73 (1983), 33-49.
- [11] S.K. Donaldson: Floer homology group in Yang-Mills theory. Cambrdge Univ. Press, Cambridge, 2002.
- [12] A. Floer: Cuplength estimates on Lagrangian intersections. Comm. Pure App. Maths., 41 (1988), 393-407.
- [13] A. Floer: A relative Morse index for the symplectic action. Comm. Pure App. Maths., 42 (1988), 335-357.
- [14] A. Floer: Morse theory for Lagrangian intersections. J. Diff. Geom., 28 (1988), 513-547.
- [15] R.W. Ghrist, P.J. Holmes and M.C. Sullivan: Knots and Links in Threedimensional Flows. LNM 1654, Springer-verlag, New York, 1997.
- [16] M. Hirsch, C. Pugh and M. Shub: Invariant Manifolds. Springer lecture notes in Maths., Springer-Verlag, Berlin, 1970.
- [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.
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Bibliografia
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