Least squares parameter estimation in chaotic differential equations

Details Least squares parameter estimation in chaotic differential equations Least squares parameter estimation in chaotic differential equations

May 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993cemda..56..353k&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 56, no. 1-2, p. 353-371.

Mathematics

Dynamical Systems

2

Boundary Value Problems, Chaos, Differential Equations, Least Squares Method, Liapunov Functions, Parameter Identification, Dynamical Systems, Jacobi Matrix Method

Scientific paper

A boundary value problem approach is considered which is based on discretizing differential equations like a boundary value problem and solving the resulting constrained least squares problem with a structure based on the generalized Gauss-Newton method (Bock, 1981). It is concluded that the boundary value problem approach is capable of recovering the parameters of the Henon-Heiles system in a variety of scenarios which differ in initial values and parameters of the simulated trajectories, noise of the Gaussian random errors, and distance of the initial guesses of the parameters from the solution. The Liapunov exponents are derived from the identified dynamical systems and are found to obey the conditions for Hamiltonian systems.

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