Title :
Trajectory Optimization for Well-Conditioned Parameter Estimation
Author :
Wilson, Andrew D. ; Schultz, Jarvis A. ; Murphey, Todd D.
Author_Institution :
Dept. of Mech. Eng., Northwestern Univ., Evanston, IL, USA
Abstract :
When attempting to estimate parameters in a dynamical system, it is often beneficial to strategically design experimental trajectories that facilitate the estimation process. This paper presents an optimization algorithm which improves conditioning of estimation problems by modifying the experimental trajectory. An objective function which minimizes the condition number of the Hessian of the least-squares identification method is derived and a least-squares method is used to estimate parameters of the nonlinear system. A software-simulated example demonstrates that an arbitrarily designed trajectory can lead to an ill-conditioned least-squares estimation problem, which in turn leads to slower convergence to the best estimate and, in the presence of experimental uncertainties, may lead to no convergence at all. A physical experiment with a robot-controlled suspended mass also shows improved estimation results in practice in the presence of noise and uncertainty using the optimized trajectory.
Keywords :
control system synthesis; least squares approximations; nonlinear control systems; optimisation; parameter estimation; trajectory control; condition number; experimental trajectory design; least squares identification method; nonlinear system; objective function; optimization algorithm; parameter estimation; robot-controlled suspended mass; trajectory optimization; Convergence; Cost function; Estimation; Heuristic algorithms; Mathematical model; Trajectory; Iterative methods in optimization; optimal control; parameter estimation;
Journal_Title :
Automation Science and Engineering, IEEE Transactions on
DOI :
10.1109/TASE.2014.2323934