On the computation of convex robust control invariant sets for nonlinear systems

Invariance of symmetric convex sets for discrete-time saturated systems

“…Many results regarding invariance and related topics have been provided in literature: see, for instance, the notable pioneering contribution [4], the works [10], [15], concerning the maximal invariant set, and [18] regarding the minimal one. The problem of obtaining invariant sets for discrete-time nonlinear systems is dealt with using ellipsoids in [16], parallelotopes in [7], and polytopes in [1], [8]. Invariance of polytopes for continuoustime nonlinear systems has been considered in [9].…”

Invariance-based analysis of cancer chemotherapy

“…In fact, Algorithm 1 is efficient and scalable to provide the maximal invariant set for all high-dimensional nonlinear systems for which the related one-step operator given by (9) is not hardly computable. Once the set of constraint states X and the initial invariant set Ω 0 are selected, Algorithm 1 is fully automatic and no parameters are needed to be selected.…”

“…{rachid.riah, mirko.fiacchini, mazen.alamir}@gipsa-lab.fr the maximal invariant set, and [18] regarding the minimal one. The problem of obtaining invariant sets for discretetime nonlinear systems is dealt with using ellipsoids in [15] and polytopes in [9]. A recent monograph on invariance and set-theory in control is [4].…”

Topology Preservation for Multi-agent Networks: Design and Implementation

“…Thus, we not only propose a new tool for decentralized control but also an easy implementable one. The practical implementation of this set theory-based control strategy [10,11] requires a minimal number of interconnections ensuring the network connectivity. It should be noted that our procedure is quite flexible and, as we shall see, additional global objectives can be addressed.…”