Optimal Trajectory Design for Well-Conditioned Parameter Estimation
| Title: | Optimal Trajectory Design for Well-Conditioned Parameter Estimation |
|---|---|
| Publication Type: | Conference Paper |
| Year of Publication: | 2013 |
| Authors: | A. D. Wilson, and T. D. Murphey |
| Conference Name: | IEEE Conference on Automation Science and Engineering (CASE) |
| Pages: | 13-19 |
| DOI: | 10.1109/CoASE.2013.6653971 |
| Abstract: | When attempting to estimate parameters in a dynamical system, it is often beneficial to systematically design the experimental trajectory. This paper presents a method of generating trajectories using an extension of a nonlinear, infinite-dimensional, projection-based trajectory optimization algorithm. A reformulated objective function is derived for the algorithm to minimize the condition number of the Hessian of the batch-least squares identification method. The batch least-squares method is then used to estimate parameters of the nonlinear system. A simulation example is used to demonstrate that an arbitrarily designed trajectory can lead to an ill-conditioned Hessian matrix in the batch-least squares method, which in turn leads to a less precise set of identified parameters. An example using Monte-Carlo simulations of both trajectories shows a reduction in the variance of identified parameters for an example cart-pendulum system. |
PDF: awilson_CASE2013.pdf
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