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Research Papers

Spectral Collocation-Based Optimization in Parameter Estimation for Nonlinear Time-Varying Dynamical Systems

[+] Author and Article Information
Venkatesh Deshmukh

Department of Mechanical Engineering, Center for Nonlinear Dynamics and Control, 800 Lancaster Avenue, Villanova, PA 19085venkatesh.deshmukh@villanova.edu

J. Comput. Nonlinear Dynam 3(1), 011010 (Dec 07, 2007) (7 pages) doi:10.1115/1.2815335 History: Received March 18, 2007; Revised July 03, 2007; Published December 07, 2007

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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Copyright © 2008 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Comparison of the state trajectories for system 21, (̱) ode45, (…..) collocation-based optimization solution with estimated x2(t) and x4(t)

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