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.
Skip Nav Destination
e-mail: venkatesh.deshmukh@villanova.edu
Article navigation
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
Search for other works by this author on:
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
Download citation file:
Get Email Alerts
Cited By
Investigation of Nonlinear Dynamic Behaviors of Vertical Rotor System Supported by Aerostatic Bearings
J. Comput. Nonlinear Dynam (January 2025)
Electric Circuit Analogs of First-Order Dual-Phase-Lag Diffusion
J. Comput. Nonlinear Dynam
Related Articles
Parametric Estimation for Delayed Nonlinear Time-Varying Dynamical Systems
J. Comput. Nonlinear Dynam (October,2011)
Erratum: “Parameter Estimation by Parameter Signature Isolation in the Time-Scale Domain” [ Journal of Dynamic Systems, Measurement, and Control, 2009, 131(4), p. 041008 ]
J. Dyn. Sys., Meas., Control (January,2011)
Adaptive Estimation of Time-Varying Parameters in Linearly Parametrized Systems
J. Dyn. Sys., Meas., Control (September,2006)
Causation Entropy Identifies Sparsity Structure for Parameter Estimation of Dynamic Systems
J. Comput. Nonlinear Dynam (January,2017)
Related Chapters
A New Algorithm for Parameter Estimation of LFM Signal
International Conference on Information Technology and Computer Science, 3rd (ITCS 2011)
ML-DC Algorithm of Parameter Estimation for Gaussian Mixture Autoregressive Model
International Conference on Computer Technology and Development, 3rd (ICCTD 2011)
Conjugate Priors with Zero Occurrences: Analyst Beware! (PSAM-0435)
Proceedings of the Eighth International Conference on Probabilistic Safety Assessment & Management (PSAM)