International audienceThis paper presents a new approach for guaranteed state estimation based on zonotopes for linear discrete-time multivariable systems with interval multiplicative uncertainties, in the presence of bounded state perturbations and noises. At each sample time, the presented approach computes a zonotope which contains the real system state. A P-radius-based criterion is minimized in order to decrease the size of the zonotope at each sample time and to obtain an increasingly accurate state estimation. The proposed approach allows one to efficiently handle the trade-off between the complexity of the computation and the accuracy of the estimation. An illustrative example is analyzed in order to highlight the advantages of the proposed state estimation technique

This paper brings a unifying point of view for several problems of nonlinear particle dynamics (including the classical Kepler, Coulomb, and Manev problems) by using the qualitative theory of dynamical systems. We consider two-body problems with potentials of the type A=r + B=r 2 , where r is the distance between particles, and A; B are real constants. Using McGehee-type transformations and exploiting the rotational symmetry speciÿc to this class of vector ÿelds, we set the equations of motion in a reduced phase space and study all possible choices of the constants A and B. In this new setting the dynamics appears elegant and simple. In the end we use the phase-space structure to tackle the question of block-regularizing collisions, which asks whether orbits can be extended beyond the collision singularity in a physically meaningful way, i.e. by preserving the continuity of the general solution with respect to initial data. HistoryThe above class of problems is over three centuries old. Newton was the ÿrst to consider central-force and two-body problems in his monumental work Principia, whose

The Manev problem (a two-body problem given by a potential of the form A/r+B/r2, where r is the distance between particles and A,B are positive constants) comprises several important physical models, having its roots in research done by Isaac Newton. We provide its analytic solution, then completely describe its global flow using McGehee coordinates and topological methods, and offer the physical interpretation of all solutions. We prove that if the energy constant is negative, the orbits are, generically, precessional ellipses, except for a zero-measure set of initial data, for which they are ellipses. For zero energy, the orbits are precessional parabolas, and for positive energy they are precessional hyperbolas. In all these cases, the set of initial data leading to collisions has positive measure.

We consider the N -body problem of celestial mechanics in spaces of nonzero constant curvature. Using the concept of locked inertia tensor, we compute the moment of inertia for systems moving on spheres and hyperbolic spheres and show that we can recover the classical definition in the Euclidean case. After proving some criteria for the existence of relative equilibria, we find a natural way to define the concept of central configuration in curved spaces using the moment of inertia, and show that our definition is formally similar to the one that governs the classical problem. The existence criteria we develop for central configurations help us provide several examples and prove that, for any given point masses on spheres and hyperbolic spheres, central configurations always exist. We end our paper with results concerning the number of central configurations that lie on the same geodesic, thus extending the celebrated theorem of Moulton to hyperbolic spheres and pointing out that it has no straightforward generalization to spheres, where the count gets complicated even in the case N = 2.

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International audienceThis paper addresses the implementation of a predictive control strategy for Unmanned Air Vehicles in the presence of bounded disturbances. The goal is to prove the feasibility of such a real-time optimization-based control design and to demonstrate its tracking capabilities for the nonlinear dynamics with respect to a reference trajectory which is pre-specified via differential flatness. In order to benefit from the computational advantages of the linear predictive control formulations, an off-line linearization strategy of the nonlinear model of the vehicle along the flat trajectory is employed. The proposed method exhibits effective performance validated through software-in-the-loop simulations and real flight tests on different Unmanned Aerial Vehicles (UAVs)

BackgroundThe authors compared two strategies for the maintenance of intraoperative normothermia during orthotopic liver transplantation (OLT): the routine forced-air warming system and the newly developed, whole body water garment.MethodsIn this prospective, randomized and open-labelled study, 24 adult patients were enrolled in one of two intraoperative temperature management groups during OLT. The water-garment group (N = 12) received warming with a body temperature (esophageal) set point of 36.8°C. The forced air-warmer group (N = 12) received routine warming therapy using upper- and lower-body forced-air warming system. Body core temperature (primary outcome) was recorded intraoperatively and during the two hours after surgery in both groups.ResultsThe mean core temperatures during incision, one hour after incision and during the skin closing were significantly higher (p < 0.05, t test with Bonferroni corrections for the individual tests) in the water warmer group compared to the control group (36.7 ± 0.1, 36.7 ± 0.2, 36.8 ± 0.1 vs 36.1 ± 0.4, 36.1 ± 0.4, 36.07 ± 0.4°C, respectively). Moreover, significantly higher core temperatures were observed in the water warmer group than in the control group during the placement of cold liver allograft (36.75 ± 0.17 vs 36.09 ± 0.38°C, respectively) and during the allograft reperfusion period (36.3 ± 0.26 vs 35.52 ± 0.42°C, respectively). In addition, the core temperatures immediately after admission to the SICU (36.75 ± 0.13 vs 36.22 ± 0.3°C, respectively) and at one hr (36.95 ± 0.13 vs 36.46 ± 0.2°C, respectively) were significantly higher in the water warmer group, compared to the control group, whereas the core temperature did not differ significantly afte two hours in ICU in both groups.ConclusionsThe investigated water warming system results in better maintenance of intraoperative normothermia than routine air forced warming applied to upper- and lower body.

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