Characterization and computation of control invariant sets for linear impulsive control systems. (February 2023)

• Record Type: Journal Article
• Authors: Sanchez, Ignacio; Louembet, Christophe; Actis, Marcelo; Gonzalez, Alejandro H.
• Is Part Of: Nonlinear analysis. Volume 47(2023)
• Publication Date: 2023-02
• Subjects: Impulsive control systems -- Admissible sets -- Invariant sets -- Model predictive control -- Polynomial positivity -- Semidefinite programming; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2022.101271
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: Impulsive control systems are suitable to describe and control a venue of real-life problems, going from disease treatment to aerospace guidance. The main characteristic of such systems is that they evolve freely in-between impulsive actions, which makes it difficult to guarantee its permanence in a given state-space region. In this work, we develop a method for characterizing and computing approximations to the maximal control invariant sets for linear impulsive control systems, which can be explicitly used to formulate a set-based model predictive controller. We approach this task using a tractable and non-conservative characterization of the admissible state sets, namely the states whose free response remains within given constraints, emerging from a spectrahedron representation of such sets for systems with rational eigenvalues. The so-obtained impulsive control invariant set is then explicitly used as a terminal set of a predictive controller, which guarantees the feasibly asymptotic convergence to a target set containing the invariant set. Necessary conditions under which an arbitrary target set contains an impulsive control invariant set (and moreover, an impulsive control equilibrium set) are also provided, while the controller performance are tested by means of two simulation examples.