Laurent Bako

Mihaly Petreczky, Laurent Bako

The paper formulates the concept of persistence of excitation for discrete-time linear switched systems, and provides sufficient conditions for an input signal to be persistently exciting. Persistence of excitation is formulated as a property of the input signal, and it is not tied to any specific identification algorithm. The results of the paper rely on realization theory and on the notion of Markov-parameters for linear switched systems.

Sérgio Waitman, Paolo Massioni, Laurent Bako et al.

This paper is concerned with incremental stability properties of nonlinear systems. We propose conditions to compute an upper bound on the incremental L2-gain and to assess incremental asymptotic stability of piecewise-affine (PWA) systems. The conditions are derived from dissipativity analysis, and are based on the construction of piecewise-quadratic functions via linear matrix inequalities (LMI) that can be efficiently solved numerically. The developments are shown to be less conservative than previous results, and are illustrated with numerical examples. In the last part of this paper, we study the connection between incremental L2-gain stability and incremental asymptotic stability. It is shown that, with appropriate observability and reachability assumptions on the input-output operator, incremental L2-gain implies incremental asymptotic stability. Finally, it is shown that the converse implication follows provided some regularity conditions on the state space representation are met.

Steeven Janny, Quentin Possamai, Laurent Bako et al.

The identification of a nonlinear dynamic model is an open topic in control theory, especially from sparse input-output measurements. A fundamental challenge of this problem is that very few to zero prior knowledge is available on both the state and the nonlinear system model. To cope with this challenge, we investigate the effectiveness of deep learning in the modeling of dynamic systems with nonlinear behavior by advocating an approach which relies on three main ingredients: (i) we show that under some structural conditions on the to-be-identified model, the state can be expressed in function of a sequence of the past inputs and outputs; (ii) this relation which we call the state map can be modelled by resorting to the well-documented approximation power of deep neural networks; (iii) taking then advantage of existing learning schemes, a state-space model can be finally identified. After the formulation and analysis of the approach, we show its ability to identify three different nonlinear systems. The performances are evaluated in terms of open-loop prediction on test data generated in simulation as well as a real world data-set of unmanned aerial vehicle flight measurements.

Laurent Bako, Madiha Nadri, Vincent Andrieu et al.

This paper discusses a general framework for designing robust state estimators for a class of discrete-time nonlinear systems. We consider systems that may be impacted by impulsive (sparse but otherwise arbitrary) measurement noise sequences. We show that a family of state estimators, robust to this type of undesired signal, can be obtained by minimizing a class of nonsmooth convex functions at each time step. The resulting state observers are defined through proximal operators. We obtain a nonlinear implicit dynamical system in term of estimation error and prove, in the noise-free setting, that it vanishes asymptotically when the minimized loss function and the to-be-observed system enjoy appropriate properties. From a computational perspective, even though the proposed observers can be implemented via efficient numerical procedures, they do not admit closed-form expressions. The paper argues that by adopting appropriate relaxations, simple and fast analytic expressions can be derived.

Quentin Possamaï, Steeven Janny, Guillaume Bono et al.

The emergence of data-driven approaches for control and planning in robotics have highlighted the need for developing experimental robotic platforms for data collection. However, their implementation is often complex and expensive, in particular for flying and terrestrial robots where the precise estimation of the position requires motion capture devices (MoCap) or Lidar. In order to simplify the use of a robotic platform dedicated to research on a wide range of indoor and outdoor environments, we present a data validation tool for ego-pose estimation that does not require any equipment other than the on-board camera. The method and tool allow a rapid, visual and quantitative evaluation of the quality of ego-pose sensors and are sensitive to different sources of flaws in the acquisition chain, ranging from desynchronization of the sensor flows to misevaluation of the geometric parameters of the robotic platform. Using computer vision, the information from the sensors is used to calculate the motion of a semantic scene point through its projection to the 2D image space of the on-board camera. The deviations of these keypoints from references created with a semi-automatic tool allow rapid and simple quality assessment of the data collected on the platform. To demonstrate the performance of our method, we evaluate it on two challenging standard UAV datasets as well as one dataset taken from a terrestrial robot.