Characterization and computation of control invariant sets for linear impulsive control systems

SANCHEZ, IGNACIO; LOUEMBET, CHRISTOPHE; ACTIS, MARCELO; GONZÁLEZ, ALEJANDRO HERNÁN

Nonlinear Analysis: Hybrid Systems

ELSEVIER

Año: 2023 vol. 47 p. 101271 - 101279

1751-570X

Impulsive control systems are suitable to describe and control a venue of real-life problems, going from disease treatment to aerospace guidance. The maincharacteristic of such systems is that they evolve freely in-between impulsive ac-tions, which makes it difficult to guarantee its permanence in a given state-spaceregion. In this work, we develop a method for characterizing and computing ap-proximations to the maximal control invariant sets for linear impulsive controlsystems, which can be explicitly used to formulate a set-based model predictivecontroller. We approach this task using a tractable and non-conservative char-acterization of the admissible state sets, namely the states whose free responseremains within given constraints, emerging from a spectrahedron representationof such sets for systems with rational eigenvalues. The so-obtained impulsivecontrol invariant set is then explicitly used as a terminal set of a predictivecontroller, which guarantees the feasibly asymptotic convergence to a target setcontaining the invariant set. Necessary conditions under which an arbitrary target set contains an impulsive control invariant set (and moreover, an impulsivecontrol equilibrium set) are also provided, while the controller performance aretested by means of two simulation examples.