Optimal initial state for fast parameter estimation in nonlinear dynamical systems

Qiaochu Li (1) , Carine Jauberthie (2) , Lilianne Denis-Vidal (3) , Zohra Cherfi (1)

1 Roberval - Roberval
2 LAAS-DISCO - Équipe DIagnostic, Supervision et COnduite
3 LMAC - Laboratoire de Mathématiques Appliquées de Compiègne

Background and Objective: This paper deals with the improvement of parameter estimation in terms of precision and computational time for dynamical models in a bounded error context. Methods: To improve parameter estimation, an optimal initial state design is proposed combined with a contractor. This contractor is based on a volumetric criterion and an original condition initializing this contractor is given. Based on a sensitivity analysis, our optimal initial state design methodology consists in searching the minimum value of a proposed criterion for the interested parameters. In our framework, the uncertainty (on measurement noise and parameters) is supposed unknown but belongs to known bounded intervals. Thus guaranteed state and sensitivity estimation have been considered. An elementary effect analysis on the number of sampling times is also implemented to achieve the fast and guaranteed parameter estimation. Results: The whole procedure is applied to a pharmacokinetics model and simulation results are given. Conclusions: The good improvement of parameter estimation in terms of computational time and precision for the case study highlights the potential of the proposed methodology.

Mots clés: Optimal initial state; Parameter estimation; Nonlinear systems; Contractor; Bounded noise; Interval analysis

Domaines: Systèmes dynamiques [math.DS]

Qiaochu Li, Carine Jauberthie, Lilianne Denis-Vidal, Zohra Cherfi. Optimal initial state for fast parameter estimation in nonlinear dynamical systems. Computer Methods and Programs in Biomedicine, 2016, ⟨10.1016/j.cmpb.2016.07.033⟩. ⟨hal-01914536⟩