Abstract : The problem of estimation in the linear regression model is studied under the hypothesis that the regressor may be excited on a limited initial interval of time only. Then the estimation solution is searched on a finite interval of time also based on the framework of finite-time or fixed-time converging dynamical systems. The robustness issue is analyzed and a short-time input-to-state stability property is introduced for fixed-time converging time-varying systems with a sufficient condition, which is formulated with the use of a Lyapunov function. Several estimation algorithms are proposed and compared with existing solutions. The performance of the estimators is demonstrated in numerical experiments.
Jian Wang, Denis Efimov, Stanislav Aranovskiy, Alexey Bobtsov. Fixed-time estimation of parameters for non-persistent excitation. European Journal of Control, Elsevier, 2020, 55, pp.24-32. ⟨10.1016/j.ejcon.2019.07.005⟩. ⟨hal-02196637⟩