1. Flatness-based control revisited: The HEOL setting
- Author
-
Join, Cédric, Delaleau, Emmanuel, and Fliess, Michel
- Subjects
Mathematics - Optimization and Control ,Electrical Engineering and Systems Science - Systems and Control ,93B25, 93B52, 93C15 - Abstract
We present the algebraic foundations of the HEOL setting, which combines flatness-based control and intelligent controllers, two advances in automatic control that have been proven in practice, including in industry. The result provides a solution to many pending questions on feedback loops concerning flatness-based control and model-free control (MFC). Elementary module theory, ordinary differential fields and the generalization of K\"ahler differentials to differential fields provide an intrinsic definition of the tangent linear system. The algebraic manipulations associated with the operational calculus lead to homeostat and intelligent controllers. They are illustrated via some computer simulations., Comment: Accepted for publication in "Comptes Rendus Math\'ematique"
- Published
- 2024