Fast interval estimation for discrete-time linear systems: An $L_1$ optimization method

Zhenhua Wang (1) , Thach Ngoc Dinh (2) , Qinghua Zhang (3) , Tarek Raissi (2) , Yi Shen (1)

1 HIT - Harbin Institute of Technology
2 CEDRIC - LAETITIA - CEDRIC. Traitement du signal et architectures électroniques
3 I4S - Statistical Inference for Structural Health Monitoring

This paper studies interval estimation for discrete-time linear systems with unknown but bounded disturbances. Inspired by the parity space approach, we propose a point estimator with fixed-time convergence property. The estimator is combined with the zonotope-based interval analysis to achieve fast interval estimation. The parameter matrix in the estimator is optimized by minimizing the length of the edges of the outer box of the error zonotope. It is formulated as L1 optimization problem and can be efficiently solved by linear programming. Comparison studies illustrate the superiority of the proposed method over existing techniques.

Mots clés: Interval estimation; zonotope; fixed-time convergence; L1 optimization; linear programming

Domaines: Automatique / Robotique

Zhenhua Wang, Thach Ngoc Dinh, Qinghua Zhang, Tarek Raissi, Yi Shen. Fast interval estimation for discrete-time linear systems: An $L_1$ optimization method. Automatica, 2022, 137, pp.110029. ⟨10.1016/j.automatica.2021.110029⟩. ⟨hal-03346716⟩