Data-based stabilization of unknown bilinear systems with guaranteed basin of attraction

2020/04/24 by Andrea Bisoffi, Claudio De Persis, Pietro Tesi
Computer Science · Engineering · Mathematics · #Advanced Control Systems Optimization #Applied mathematics #Artificial intelligence #Attraction #Bilinear interpolation #Block (permutation group theory) #Computer science #Control (management) #Control Systems and Identification #Control theory (sociology) #Controller (irrigation) #Fault Detection and Control Systems #Ideal (ethics) #Law #Mathematical optimization #Mathematics #Nonlinear system #Scalar (mathematics) #Statistics #cs.SY #eess.SY #math.DS

paper · pdf · doi:10.1016/j.sysconle.2020.104788

published as Systems & Control Letters 145 (2020) 104788

arxiv created 2020/04/24 · openalex publication_date 2020/10/01 · arxiv updated 2020/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Motivated by the goal of having a building block in the design of direct data-driven controllers for nonlinear systems, we show how, for an unknown discrete-time bilinear system, the data collected in an offline open-loop experiment enable us to design a feedback controller and provide a guaranteed underapproximation of its basin of attraction. Both can be obtained by solving a linear matrix inequality for a fixed scalar parameter, and possibly iterating on different values of that parameter. The results of this data-based approach are compared with the ideal case when the model is known perfectly.

Citations

• From model-based control to data-driven control: Survey, classification and perspective
• Model-free control and intelligent PID controllers: towards a possible trivialization of nonlinear control?
• End to End Learning for Self-Driving Cars
• Safe Model-based Reinforcement Learning with Stability Guarantees
• A note on persistency of excitation