This paper proposes a novel autonomous navigation method for Mars-orbiting probes. Satellite-to-satellite tracking (SST) between two probes is generally deemed to involve autonomous measurements with no dependence on any external observation sites on the Earth. For the conventional two-body dynamic model, it is well known that the orbit states cannot be estimated by merely using such SST measurements. Considering the effects of third-body gravitation perturbation and the weak Mars tesseral harmonics perturbation, autonomous navigation with SST measurements alone becomes weakly observable and may be achieved by some nonlinear filtering techniques. Two significant improvements are made to mitigate the nonlinearity brought by the dynamic models. First, singularity-avoiding orbit elements are selected to represent the dynamic models in order to reduce the intensity of the nonlinearity which cannot be overcome by the traditional position–velocity state expression. Second, the unscented Kalman filter method is effectively utilised to avoid the linearised errors calculated by its extended Kalman filter counterpart which may exceed the tesseral harmonics perturbation. A constellation, consisting of one low-orbit probe and one high-orbit probe, is designed to realise the autonomous orbit determination of both participating Mars probes. A reliable navigation solution is successfully obtained by Monte Carlo simulation runs. It shows that the errors of the semimajor axes of the two Mars probes are less than 10 m and the position errors are less than 1 km.

In this article, we study the observability (or equivalently, the controllability) of some subelliptic evolution equations depending on their step. This sheds light on the speed of propagation of these equations, notably in the ‘degenerated directions’ of the subelliptic structure.

First, for any $\gamma \geq 1$ , we establish a resolvent estimate for the Baouendi–Grushin-type operator $\Delta _{\gamma }=\partial _x^2+\left \lvert x\right \rvert ^{2\gamma }\partial _y^2$ , which has step $\gamma +1$ . We then derive consequences for the observability of the Schrödinger-type equation $i\partial _tu-\left (-\Delta _{\gamma }\right )^{s}u=0$ , where $s\in \mathbb N$ . We identify three different cases: depending on the value of the ratio $(\gamma +1)/s$ , observability may hold in arbitrarily small time or only for sufficiently large times or may even fail for any time.

As a corollary of our resolvent estimate, we also obtain observability for heat-type equations $\partial _tu+\left (-\Delta _{\gamma }\right )^su=0$ and establish a decay rate for the damped wave equation associated with $\Delta _{\gamma }$ .

One argument against secret ballots is that such procedures lead to more selfish voting behavior and that public voting can increase prosocial voting and the likelihood of prosocial outcomes when voters are not subject to intimidation and coercion from outside interests. We investigate this supposition as well as voter preferences over observability in voting in this context. We find that voters are significantly more likely to choose unselfishly when voting is public. These differences in behavior advantage prosocial choices in elections (by 27%) when voting is public. Moreover, voters appear to recognize these differences and a substantial minority of voters whose selfish preference is not the prosocial choice willingly choose public voting even though the likely outcome will be costly to themselves.

Precise autonomous navigation remains a substantial challenge to all underwater platforms. Inertial Measurement Units (IMU) and Doppler Velocity Logs (DVL) have complementary characteristics and are promising sensors that could enable fully autonomous underwater navigation in unexplored areas without relying on additional external Global Positioning System (GPS) or acoustic beacons. This paper addresses the combined IMU/DVL navigation system from the viewpoint of observability. We show by analysis that under moderate conditions the combined system is observable. Specifically, the DVL parameters, including the scale factor and misalignment angles, can be calibrated in-situ without using external GPS or acoustic beacon sensors. Simulation results using a practical estimator validate the analytic conclusions.

In this work, we investigate a quaternion-based formulation of 3D Simultaneous Localization and Mapping with Extended Kalman Filter (EKF-SLAM) using relative pose measurements. We introduce a discrete-time derivation that avoids the normalization problem that often arises when using unit quaternions in Kalman filter and we study its observability properties. The consistency of the estimation errors with the corresponding covariance matrices is also evaluated. The approach is further tested on real data from the Rawseeds dataset and it is applied within a delayed-state EKF architecture for estimating a dense 3D map of an unknown environment. The contribution is motivated by the possibility of abstracting multi-sensorial information in terms of relative pose measurements and for its straightforward extensions to the multi robot case.

This article aims at studying the controllability of a simplified fluid structure interaction model derived and developed in [C. Conca, J. Planchard and M. Vanninathan, RAM: Res. Appl. Math. John Wiley & Sons Ltd., Chichester (1995); J.-P. Raymond and M. Vanninathan, ESAIM: COCV 11 (2005) 180–203; M. Tucsnak and M. Vanninathan, Systems Control Lett. 58 (2009) 547–552]. This interaction is modeled by a wave equation surrounding a harmonic oscillator. Our main result states that, in the radially symmetric case, this system can be controlled from the outer boundary. This improves previous results [J.-P. Raymond and M. Vanninathan, ESAIM: COCV 11 (2005) 180–203; M. Tucsnak and M. Vanninathan, Systems Control Lett. 58 (2009) 547–552]. Our proof is based on a spherical harmonic decomposition of the solution and the so-called lateral propagation of the energy for 1d waves.

Local and global Carleman estimates play a central role in the study of some partial differential equations regarding questions such as unique continuation and controllability. We survey and prove such estimates in the case of elliptic and parabolic operators by means of semi-classical microlocal techniques. Optimality results for these estimates and some of their consequences are presented. We point out the connexion of these optimality results to the local phase-space geometry after conjugation with the weight function. Firstly, we introduce local Carleman estimates for elliptic operators and deduce unique continuation properties as well as interpolation inequalities. These latter inequalities yield a remarkable spectral inequality and the null controllability of the heat equation. Secondly, we prove Carleman estimates for parabolic operators. We state them locally in space at first, and patch them together to obtain a global estimate. This second approach also yields the null controllability of the heat equation.

The goal of this article is to analyze the observability properties for a space semi-discrete approximation scheme derived from a mixed finite element method of the 1d wave equation on nonuniform meshes. More precisely, we prove that observability properties hold uniformly with respect to the mesh-size under some assumptions, which, roughly, measures the lack of uniformity of the meshes, thus extending the work [Castro and Micu, Numer. Math.102 (2006) 413–462] to nonuniform meshes. Our results are based on a precise description of the spectrum of the discrete approximation schemes on nonuniform meshes, and the use of Ingham's inequality. We also mention applications to the boundary null controllability of the 1d wave equation, and to stabilization properties for the 1d wave equation. We finally present some applications for the corresponding fully discrete schemes, based on recent articles by the author.

In this paper, we prove the genericity of the observability for discrete-time systems with more outputs than inputs.

In this paper, we consider general nonlinear systems with observations, containing a (single) unknown function φ. We study the possibility to learn about this unknown function via the observations: if it is possible to determine the [values of the] unknown function from any experiment [on the set of states visited during the experiment], and for any arbitrary input function, on any time interval, we say that the system is “identifiable”. For systems without controls, we give a more or less complete picture of what happens for this identifiability property. This picture is very similar to the picture of the “observation theory” in [7]: Contrarily to the case of the observability property, in order to identify in practice, there is in general no hope to do something better than using “approximate differentiators”, as show very elementary examples. However, a practical methodology is proposed in some cases. It shows very reasonable performances.
As an illustration of what may happen in controlled cases, we consider the equations of a biological reactor, [2,4], in which a population is fed by some substrate. The model heavily depends on a “growth function”, expressing the way the population grows in presence of the substrate. The problem is to identify this “growth function”. We give several identifiability results, and identification methods, adapted to this problem.

We consider the Laplace equation in a smooth bounded domain. We prove logarithmic estimates, in the sense of John [5] of solutions on a part of the boundary or of the domain without known boundary conditions. These results are established by employing Carleman estimates and techniques that we borrow from the works of Robbiano [8,11]. Also, we establish an estimate on the cost of an approximate control for an elliptic model equation.

We are extending to linear recurrent codes, i.e., to time-varying convolutional codes, most of the classic structural properties of fixed convolutional codes. We are also proposing a new connection between fixed convolutional codes and linear block codes. These results are obtained thanks to a module-theoretic framework which has been previously developed for linear control.

This paper addresses the problem of identifying the uncertainties present in a robotic contact situation. These uncertainties are errors and misalignments of an object with respect to its ideal position. The paper describes how to solve for the errors caused during grasping and errors present when coming into contact with the environment. A force sensor is used together with Kalman Filters to solve for all the uncertainties. The straightforward use of a force sensor and the Kalman Filters is found to be effective in finding only some of the uncertainties in robotic contact. The other uncertainties form dependencies that cannot be estimated in this manner. This dependency brings about the problem of observability. To make the unobservable uncertainties observable a sequence of contacts are used. The error covariance matrix of the Kalman Filter (KF) is used to obtain new contacts that are required to solve for all the uncertainties completely. There is complete freedom in choosing which unobservable quantity to be excited in forming the next contact. The paper describes how these new contacts can be randomly executed. A two dimensional contact situation will be used to demonstrate the effectiveness of the method. Experimental data are also presented to prove the validity of the procedure. Due to the non-linear relationship between the uncertainties and the forces, an Extended Kalman Filter (EKF) has been used.

We prove an observability estimate for awave equation with rapidly oscillating density,in a bounded domain with Dirichlet boundary condition.

For smooth or real-analytic single-input, control-affine, non-linear systems, with at least two ouputs, observability for any input ofa given class is generic. This class can be either the class of inputs bounded with their derivatives up to a certain order, or the class ofpolynomial inputs with bounded degree.