Stochastic identification of minimum set of dynamics parameters that has small sensitivity on controlled velocity field in state-space

Abstract

Accurate identification of minimum set of dynamics parameters is required for high-precision and high-speed motion control. The identification uses the dynamical model and its motion data. This motion data does not always satisfy the equations in the dynamical model because of unmodeled dynamics and unexpected noise. The least squares method is generally used for approximated model. It may well satisfy the equations in the dynamical model, however, the optimality as a model for control system design has to be discussed. In this paper, we propose a stochastic identification method of minimum set of dynamic parameters. In conventional least squares method, the error of dynamic equation is assumed to be white gaussian and its square mean is minimized while in the proposed method, the error is assumed to be due to parameter fluctuation, and its covariance is optimized so that the sensitivity of velocity field in the state space with respect to dynamic parameter is small, which means advantageous parameter for controlled system. The simulation and experimental results show the effectiveness of the proposed method.

Keywords

• parameter identification
• sensitivity analysis
• inverted pendulum
• vector field
• dynamical system