Composite Immersion and Invariance Based Adaptive Attitude Control of Asteroid-Orbiting Spacecraft in Elliptic Orbit

This paper proposes a new composite noncertainty-equivalence adaptive (CNCEA) control system for the attitude (roll, pitch, and yaw angle) control of a spacecraft in an orbit around a uniformly rotating asteroid based on the immersion and invariance (I&I) theory. For the design, it is assumed that the asteroid's gravitational parameters and the spacecraft's inertia matrix are not known. In contrast to certainty-equivalence adaptive (CEA) or noncertainty-equivalence adaptive (NCEA) systems, the CNCEA attitude control system's composite identifier uses the attitude angle tracking error, a nonlinear state-dependent vector function, and model prediction error for parameter estimation. The Lyapunov analysis shows that in the closed-loop system, the Euler angles asymptotically track the reference attitude trajectories. Interestingly, there exist two parameter error-dependent attractive manifolds, to which the closed-loop system's trajectories converge. Moreover, the composite identifier using two types of error signals provides stronger stability properties in the closed-loop system. Simulation results are presented for the attitude control of a spacecraft orbiting in the vicinity of the asteroid 433 Eros. These results show precise nadir pointing attitude regulation, despite uncertainties in the system.

Multiplicatively dependent vectors with coordinates algebraic numbers

International audience We shall prove that close to each point in \mathbb{C}^n with coordinates of comparable size there is a point (t_1 , ... , t_n) with the property that no multiplicatively dependent vector (u_1 , ... , u_n) with coordinates which are algebraic numbers of height at most H and degree at most d is very close to (t_1 , ... , t_n).

Seasonal Soybean Price Transmission between the U.S. and Brazil Using the Seasonal Regime-Dependent Vector Error Correction Model

Soybean production and trade in the U.S. and Brazil are seasonal. Our research question is whether the seasonal tendencies cause the price relationship between U.S. and Brazilian soybean prices. Therefore, the objective is to test for seasonality in the price transmission between the U.S. and Brazil soybean prices using the seasonal regime-dependent vector error correction model (VECM). Our results show that the speed of the adjustment for the U.S. soybean price in the first half of the year is greater than the speed of the adjustment for the Brazilian soybean price. However, the pattern of their responses becomes the reverse in the second half of the year. The component share calculated by the result of the VECM with seasonal effects indicates that the U.S. dominates the world soybean market during the second half of the year while Brazil is dominant in the soybean market in the first half of the year. These results give us an important finding that we could not find using the VECM without seasonal effects. Finally, our results imply that the seasonal pattern of production in the U.S. and Brazil could cause the sustainability of the supply chain in the world soybean market.

On the generalization of the Darboux theorem

Darboux theorem to more general context of Frechet manifolds we face an obstacle: in general vector fields do not have local flows. Recently, Fr\'{e}chet geometry has been developed in terms of projective limit of Banach manifolds. In this framework under an appropriate Lipchitz condition The Darboux theorem asserts that a symplectic manifold $(M^{2n},\omega)$ is locally symplectomorphic to $(R^{2n}, \omega_0)$, where $\omega_0$ is the standard symplectic form on $R^{2n}$. This theorem was proved by Moser in 1965, the idea of proof, known as the Moser’s trick, works in many situations. The Moser tricks is to construct an appropriate isotopy $ \ff_t $ generated by a time-dependent vector field $ X_t $ on $M$ such that $ \ff_1^{*} \omega = \omega_0$. Nevertheless, it was showed by Marsden that Darboux theorem is not valid for weak symplectic Banach manifolds. However, in 1999 Bambusi showed that if we associate to each point of a Banach manifold a suitable Banach space (classifying space) via a given symplectic form then the Moser trick can be applied to obtain the theorem if the classifying space does not depend on the point of the manifold and a suitable smoothness condition holds. If we want to try to generalize the local flows exist and with some restrictive conditions the Darboux theorem was proved by Kumar. In this paper we consider the category of so-called bounded Fr\'{e}chet manifolds and prove that in this category vector fields have local flows and following the idea of Bambusi we associate to each point of a manifold a Fr\'{e}chet space independent of the choice of the point and with the assumption of bounded smoothness on vector fields we prove the Darboux theorem.

Highly efficient and super-bright neurocircuit tracing using vector mixing-based virus cocktail

ABSTRACTMapping the detailed cell-type-specific input networks and neuronal projectomes are essential to understand brain function in normal and pathological states. However, several properties of current tracing systems, including labeling sensitivity, trans-synaptic efficiencies, reproducibility among different individuals and different Cre-driver animals, still remained unsatisfactory. Here, we developed MAP-ENVIVIDERS, a recombinase system-dependent vector mixing-based strategy for highly efficient neurocircuit tracing. MAP-ENVIVIDERS enhanced tracing efficiency of input networks across the whole brain, with over 10-fold improvement in diverse previously poor-labeled input brain regions and particularly, up to 70-fold enhancement in brainstem compared with the current standard rabies-virus-mediated systems. MAP-ENVIVIDERS was over 10-fold more sensitive for cell-type-specific labeling than previous strategies, enabling us to capture individual cell-type-specific neurons with extremely complex axonal branches and presynaptic axonal boutons, both about one order of magnitude than previously reported and considered. MAP-ENVIVIDERS provides powerful tools for deconstructing novel input/output circuitry towards functional studies and disorders-related mechanisms.