A nonlinear observer for estimating parameters in dynamic systems

A new algorithm for estimating constant parameters in a dynamic system is presented. A generalization of a recently developed method for estimating the coefficient of friction in a dynamic system; the algorithm is a reduced-order observer having two nonlinear functions, one being the Jacobian of the other. If the dynamics of the system are affine in the parameters to be estimated, the error in estimation of these parameters satisfies a linear, time-varying homogeneous differential equation. By proper choice of the nonlinear function in the observer, it is possible to achieve asymptotic stability of the estimation error. Although the algorithm is derived on the assumption that the process state can be measured, it can be used to estimate the parameters concurrently with the state. Example applications, including one of adaptive control, are presented.