System identification: theory for the user
System identification: theory for the user
Identification and application of bounded-parameter models
Automatica (Journal of IFAC)
Maximum likelihood estimators and worst case optimal algorithms for system identification
Systems & Control Letters
System identification
Parameter estimation algorithms for a set-membership description of uncertainty
Automatica (Journal of IFAC)
Optimal estimation theory for dynamic systems with set membership uncertainty: an overview
Automatica (Journal of IFAC)
On the value of information in system identification-Bounded noise case
Automatica (Journal of IFAC)
Paper: Bounded-error parameter estimation: Noise models and recursive algorithms
Automatica (Journal of IFAC)
Brief Recursive algorithms for inner ellipsoidal approximation of convex polytopes
Automatica (Journal of IFAC)
The size of the membership-set in a probabilistic framework
Automatica (Journal of IFAC)
Direct feedback control design for nonlinear systems
Automatica (Journal of IFAC)
| Hi-index | 22.15 |
In this paper, we study the convergence properties of the membership set for system identification in the presence of unknown but bounded noise. Besides the classical pointwise noise model, we also analyze the so-called window and average models. Two different scenarios are considered: (1) the bound (tight or overestimated) is known; (2) the bound is unknown and has to be estimated from measurement data. Under some probabilistic assumptions on the noise sequence and with the persistent excitation regressor, in the first case we prove that the diameter of the associated membership sets converges to zero with probability one if the noise bound is tight. If the bound is overestimated, we compute upper bounds for the diameter which are stated in terms of the difference between the true and the over-estimated bound. In the second case, we show that the estimates of the bound converge to the true but unknown noise bound.