A constructive optimization algorithm using Chebyshev spectral collocation and quadratic programming is proposed for unknown parameter estimation in nonlinear time-varying dynamic system models to be constructed from available data. The parameters to be estimated are assumed to be identifiable from the data, which also implies that the assumed system models with known parameter values have a unique solution corresponding to every initial condition and parameter set. The nonlinear terms in the dynamic system models are assumed to have a known form, and the models are assumed to be parameter affine. Using an equivalent algebraic description of dynamical systems by Chebyshev spectral collocation and data, a residual quadratic cost is set up, which is a function of unknown parameters only. The minimization of this cost yields the unique solution for the unknown parameters since the models are assumed to have a unique solution for a particular parameter set. An efficient algorithm is presented stepwise and is illustrated using suitable examples. The case of parameter estimation with incomplete or partial data availability is also illustrated with an example.
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e-mail: venkatesh.deshmukh@villanova.edu
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January 2008
Research Papers
Spectral Collocation-Based Optimization in Parameter Estimation for Nonlinear Time-Varying Dynamical Systems
Venkatesh Deshmukh
Venkatesh Deshmukh
Department of Mechanical Engineering,
e-mail: venkatesh.deshmukh@villanova.edu
Center for Nonlinear Dynamics and Control
, 800 Lancaster Avenue, Villanova, PA 19085
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Venkatesh Deshmukh
Department of Mechanical Engineering,
Center for Nonlinear Dynamics and Control
, 800 Lancaster Avenue, Villanova, PA 19085e-mail: venkatesh.deshmukh@villanova.edu
J. Comput. Nonlinear Dynam. Jan 2008, 3(1): 011010 (7 pages)
Published Online: December 7, 2007
Article history
Received:
March 18, 2007
Revised:
July 3, 2007
Published:
December 7, 2007
Citation
Deshmukh, V. (December 7, 2007). "Spectral Collocation-Based Optimization in Parameter Estimation for Nonlinear Time-Varying Dynamical Systems." ASME. J. Comput. Nonlinear Dynam. January 2008; 3(1): 011010. https://doi.org/10.1115/1.2815335
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