Sum-of-Squares methods for controlled invariant sets with applications to model-predictive control. (May 2020)

• Record Type: Journal Article
• Authors: Legat, Benoît; Tabuada, Paulo; Jungers, Raphaël M.
• Is Part Of: Nonlinear analysis. Volume 36(2020)
• Publication Date: 2020-05
• Subjects: Controller synthesis -- Set invariance -- LMIs -- Scalable methods; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2020.100858
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: We develop a method for computing controlled invariant sets of discrete-time affine systems using Sum-of-Squares programming. We apply our method to the controller design problem for switching affine systems with polytopic safe sets but our work also improves the state of the art for the particular case of LTI systems. The task is reduced to a semidefinite programming problem by enforcing an invariance relation in the dual space of the geometric problem. The paper ends with an application to safety critical model predictive control.