Search

International audience; This paper considers the Multiplici- ty-Induced-Dominancy (MID) property for second order neutral time-delay differential equations. Necessary and sufficient conditions for the exis- tence of a root of maximal multiplicity are given in terms of this root and the parameters (includ- ing the delay) of the given equation. Links with dominancy of this root and with the exponential stability property of the solution of the consid- ered equations are given. Finally, we illustrate the obtained results on the classical oscillator control problem.

The angle $\gamma$ of the Cabibbo--Kobayashi--Maskawa unitarity triangle is a benchmark parameter of the Standard Model of particle physics. A method to determine $\gamma$ from $B^{\pm} \to D K^{\pm}$ with subsequent $D \to K_{\rm S}^0\pi^+\pi^-$ or similar multibody decays has been proven to provide good sensitivity. We review the first discussions on the use of this technique, and its impact subsequently. We propose that this approach should be referred to as the BPGGSZ method.

The mixing of neutral mesons is sensitive to some of the highest scales probed in laboratory experiments. In light of the planned LHCb Upgrade II, a possible upgrade of Belle II, and the broad interest in flavor physics in the tera-Z phase of the proposed FCC-ee program, we study constraints on new physics contributions to Bd and Bs mixings which can be obtained in these benchmark scenarios. We explore the limitations of this program, and identify the measurement of |Vcb| as one of the key ingredients in which progress beyond current expectations is necessary to maximize future sensitivity. We speculate on possible solutions to this bottleneck. Given the current tension with the standard model (SM) in semileptonic B decays, we explore how its resolution may impact the search for new physics in mixing. Even if new physics has the same Cabibbo-Kobayashi-Maskawa and loop suppressions of flavor changing processes as the SM, the sensitivity will reach 2 TeV, and it can be much higher if any SM suppressions are lifted. We illustrate the discovery potential of this program.

International audience; This work revisits recent results on maximal multiplicity induced-dominancy for spectral values in reduced-order time-delay Systems and extends it to the general class of second-order retarded differential equations. A parametric multiplicity-induced-dominancy property is characterized, allowing to a delayed stabilizing design with reduced complexity. As a matter of fact, the approach is merely a delayed-output-feedback where the candidates' delays and gains result from the manifold defining the maximal multiplicity of a real spectral value, then, the dominancy is shown using the argument principle. Sensitivity of the control design with respect to the parameters uncertainties/variation is discussed. Various reduced order examples illustrate the applicative perspectives of the approach.; Ce travail revisite les résultats récents sur la dominance induite par la multiplicité maximale des valeurs spectrales dans les systèmesà retard d'ordre réduit et l'étendà la classe la plus générale générale deséquations différentielles de second ordre impliquant un retard. La propriété de dominance induite par la multiplicité est paramétriquement caractérisée, permettant la conception de loi de commande retardée, stabilisante età complexité réduite. En effet, l'approche consiste simplement en un retour de sortie retardé dans lequel les retards et les gains des candidats résultent de la variété définissant la multiplicité maximale d'une valeur spectrale réelle, puis la dominance est montrée en utilisant le principe de l'argument. La sensibilité de la conception de la commande aux paramètres incertains/variant est discutée. Divers exemples d'ordre réduit illustrent les perspectives applicatives de l'approche.

International audience; Recent results on maximal multiplicity induced-dominancy for spectral values in reduced-order Time-Delay Systems naturally apply in controllers design. As a matter of fact, the approach is merely a delayed-output-feedback where the candidates' delays and gains result from the manifold defining the maximal multiplicity of a real spectral value, then, the dominancy is shown using the argument principle. Various reduced order examples illustrate the applicative perspectives of the approach.

In this paper we account for the numerical error introduced by the Finite Element approximation of the shape gradient to construct a guaranteed shape optimization method. We present a goal-oriented strategy inspired by the complementary energy principle to construct a constant-free, fully-computable a posteriori error estimator and to derive a certified upper bound of the error in the shape gradient. The resulting Adaptive Boundary Variation Algorithm (ABVA) is able to identify a genuine descent direction at each iteration and features a reliable stopping criterion for the optimization loop. Some preliminary numerical results for the inverse identification problem of Electrical Impedance Tomography are presented.

In most shape optimization problems, the optimal solution does not belong to the set of genuine shapes but is a composite structure. The homogenization method consists in relaxing the original problem thereby extending the set of admissible structures to composite shapes. From the numerical viewpoint, an important asset of the homogenization method with respect to traditional geometrical optimization is that the computed optimal shape is quite independent from the initial guess (at least for the compliance minimization problem). Nevertheless, the optimal shape being a composite, a post-treatement is needed in order to produce an almost optimal non-composite (i.e. workable) shape. The classical approach consists in penalizing the intermediate densities of material, but the obtained result deeply depends on the underlying mesh used and the level of details is not controllable. In a previous work, we proposed a new post-treatement method for the compliance minimization problem of an elastic structure. The main idea is to approximate the optimal composite shape with a locally periodic composite and to build a sequence of genuine shapes converging toward this composite structure. This method allows us to balance the level of details of the final shape and its optimality. Nevertheless, it was restricted to particular optimal shapes, depending on the topological structure of the lattice describing the arrangement of the holes of the composite. In this article, we lift this restriction in order to extend our method to any optimal composite structure for the compliance minimization problem.

One of the questions of ongoing interest for linear time-delay systems is to determine conditions on the equation's parameters that guarantee the exponential stability of solutions. In general, it is quite a challenge to establish conditions on the parameters of the system in order to guarantee such a stability. One of the effective approaches in the stability analysis of time-delay systems is the frequency domain approach. In the Laplace domain, the stability analysis amounts to study the distribution of characteristic quasipolynomial functions' roots. Once the stability of a delay system has been proven, it is important to characterize the exponential decay rate of the solutions of such systems. In the frequency domain, this decay rate corresponds to the dominant spectral value. Recent works emphasized the link between maximal multiplicity and dominant roots. Indeed, conditions for a given multiple root to be dominant are investigated, this property is known as Multiplicity-Induced-Dominancy (MID). In this dissertation, three topics related to the MID property are investigated. Firstly, the effect of multiple roots with admissible multiplicities exhibiting, under appropriate conditions, the validity of the MID property for second-order neutral time-delay differential equations with a single delay is explored. The stabilization of the classical oscillator benefits from the obtained results. Secondly, the effects of time-delays on the stability of Unmanned Aerial Vehicles (UAVs) is exploited. In this regard, a symbolic/numeric application of the MID property in the control of UAV rotorcrafts featuring time-delays is provided. Lastly, the stabilization of a rolling balance board by means of the MID property is considered.; Une des questions d'intérêt pour les systèmes linéaires à retard est de déterminer les conditions sur les paramètres de l'équation qui garantissent la stabilité exponentielle des solutions. En général, c'est un véritable défi d'établir des conditions sur les paramètres du système afin de garantir une telle stabilité. L'une des approches efficaces dans l'analyse de stabilité des systèmes à retard est l'approche fréquentielle. Dans le domaine de Laplace, l'analyse de stabilité revient à étudier la distribution des racines des fonctions quasipolynomiales caractéristiques. Une fois la stabilité d'un système à retard prouvée, il est important de caractériser le taux de décroissance exponentielle des solutions de ces systèmes. Dans le domaine fréquentiel, ce taux de décroissance correspond à la valeur spectrale dominante. Des travaux récents ont mis en évidence le lien entre la multiplicité maximale et les racines dominantes. En effet, les conditions pour qu'une racine multiple donnée soit dominante sont étudiées, cette propriété est connue sous le nom de Multiplicity-Induced-Dominancy (MID). Dans cette thèse, trois sujets liés à la propriété MID sont étudiés. Premièrement, l'effet des racines multiples avec des multiplicités admissibles présentant, sous des conditions appropriées, la validité de la propriété MID pour les équations différentielles neutres du second ordre avec un seul retard est exploré. La stabilisation de l'oscillateur classique bénéficie des résultats obtenus. Deuxièmement, les effets des retards sur la stabilité des véhicules aériens sans pilote (UAV) sont exploités. À cet égard, une application symbolique/numérique de la propriété MID dans le contrôle des drones à rotor avec des retards est fournie. Enfin, la stabilisation d'une balance à roulettes par le biais de la propriété MID est considérée.