Stable on-line parameter identification algorithms for systems with non-parametric uncertainties and disturbances

Abstract

An on-line parameter identification problem is formulated for linear time-invariant continuous-time systems with bounded input/output disturbances as well as non-parametric uncertainties characterized either by H² or H^∞ norms. Based on the formulation, a switching type gradient algorithm is proposed to estimate the parameters of the system from the available input-output data. In spite of the existence of non-parametric uncertainties and disturbances, this on-line algorithm guarantees that the estimation error is monotonically decreasing with respect to time, and the parameter estimate is convergent to a steady-state value under a mild condition. Furthermore, the algorithm is stable in the sense that the estimation error will converge to zero as both non-parametric uncertainties and disturbances gradually diminish. To evaluate the accuracy of the identified parameters, an upper bound on the estimation error is given.