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)

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.

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