Optimal Trajectory Design for Well-Conditioned Parameter Estimation

TitleOptimal Trajectory Design for Well-Conditioned Parameter Estimation
Publication TypeConference Paper
Year of Publication2013
AuthorsWilson, A. D., and T. D. Murphey
Conference NameIEEE Conference on Automation Science and Engineering (CASE)
Pages13-19
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.

DOI10.1109/CoASE.2013.6653971
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