Brigitte D'Andrea Novel

• Institut Mines-Télécom

The paper is concerned with the finite-time stabilization of a coupled PDE-ODE system describing the motion of an overhead crane with a flexible cable. The dynamics of the flexible cable is described by the wave equation with a variable coefficient which is an affine function of the curvilinear abscissa along the cable. Using several changes of var...

The paper is concerned with the finite-time stabilization of a hybrid PDE-ODE system describing the motion of an overhead crane with a flexible cable. The dynamics of the flexible cable is described by the wave equation with a variable coefficient which is an affine function of the curvilinear abscissa along the cable. Using several changes of vari...

This paper deals with an application of active control of percussion instruments. Our setup consists of a tom-tom drum with a circular membrane, a cylindrical cavity and a circular rigid wall on which a loudspeaker is mounted. The current applied to the loudspeaker is controlled in order to modify the frequencies of the axisymmetric drum membrane m...

Vehicles evolving in harsh terrains are subject to physical phenomena with a much more important impact than in the case of road vehicle. The main problem we have to face is tire slippery which has to be taken into account when designing the control law to ensure an accurate tracking. In this paper we present a controller for cars equipped with 4 s...

A tuning procedure for the model-free control paradigm introduced in Fliess and Join (2013) is proposed. This controller requires an estimate of the system dynamics usually obtained using an ALIEN filter, presented in Fliess and Sira-Ramírez (2003). Several implementation issues of this ALIEN filter, such as the order of the numerical quadrature, a...

The paper is concerned with the finite-time stabilization of a hybrid PDE-ODE system which may serve as a model for the motion of an overhead crane with a flexible cable. The dynamics of the flexible cable is assumed to be described by the wave equation with constant coefficients. Using a nonlinear feedback law inspired by those given by Haimo (SIA...

This paper concerns the small-time stabilization of some classes of mechanical systems which are not stabilizable by means of at least continuous state feedback laws. This is the case of nonholonomic mechanical systems, an example being the unicycle robot, or for underactuated mechanical systems, an example being the slider. Explicit time-varying f...

The paper is concerned with the finite-time stabilization of a hybrid PDE-ODE system which may serve as a model for the motion of an overhead crane with a flexible cable. The dynamics of the flexible cable is assumed to be described by the wave equation with constant coefficients. Using a nonlinear feedback law inspired by those given by Haimo in [...

This paper proposes to combine a 10Hz motion planner based on a kinematic bicycle Model Predictive Control (MPC) and a 100Hz closed-loop Proportional-Integral-Derivative (PID) controller to cope with normal driving situations. Its novelty consists in ensuring the feasibility of the computed trajectory by the motion planner through a limitation of t...

On s’intéresse au contrôle d’un oscillateur passif, avec pour objectif de le stabiliser sur un état d’équilibre cible. Dans cet article, deux approches de l’automatique sont examinées, comparées, puis associées. La première approche repose sur le formalisme des Systèmes Hamiltoniens à Ports (systèmes passifs admettant un bilan de puissance équilib...

This work deals with the design method of robust switched H∞PI observer-based control for switched uncertain systems with external disturbances. All sufficient conditions for the robust stability of the closed-loop systems are established by using switched Lyapunov function and LMI/LME framework. Its performances are demonstrated through the vehicl...

This communication presents a longitudinal model-free control approach for computing the wheel torque command to be applied on a vehicle. This setting enables us to overcome the problem of unknown vehicle parameters for generating a suitable control law. An important parameter in this control setting is made time-varying for ensuring finite-time st...

This paper deals with global chassis control of automotive vehicles. It focuses on the coordination of suspension and steering/braking vehicle controllers based on the interaction between the vertical and lateral behaviors of the vehicle. It is shown that the lateral acceleration and resulting roll motion of the car generate load transfers that con...

In this paper, the problem of tracking desired longitudinal and lateral motions for a vehicle is addressed. Let us point out that a "good" modeling is often quite difficult or even impossible to obtain. It is due for example to parametric uncertainties, for the vehicle mass, inertia or for the interaction forces between the wheels and the road pave...

In this paper, the problem of tracking desired longitudinal and lateral motions for a vehicle is addressed. Let us point out that a "good" modeling is often quite difficult or even impossible to obtain. It is due for example to parametric uncertainties, for the vehicle mass, inertia or for the interaction forces between the wheels and the road pave...

Recent investigations on the longitudinal and lateral control of wheeled autonomous vehicles are reported. Flatness-based techniques are first introduced via a simplified model. It depends on some physical parameters, like cornering stiffness coefficients of the tires, friction coefficient of the road, ..., which are notoriously difficult to identi...

Ce papier présente les différentes modélisations d'un véhicule afin d'élaborer une architecture de commande pour des véhicules autonomes dans le cadre des Systèmes de Transport Intelligents (STI). Cette architecture doit être cohérente avec la situation de conduite, notamment lors de situations d'urgence déclenchées par un événement difficilement p...

Recent investigations on the longitudinal and lateral control of wheeled autonomous vehicles are reported. Flatness-based techniques are first introduced via a simplified model. It depends on some physical parameters, like cornering stiffness coefficients of the tires, friction coefficient of the road, ..., which are notoriously difficult to identi...

This paper presents a switched H^ optimal control for a class of discrete-time switched linear systems. All sufficient conditions of the existence of the control law are proved and given in terms of LMI for any switching. Moreover, the proofs are established using an H^ norm and switched Lyapunov functions. Its performances are shown through a stee...

A new model-free setting and the corresponding "intelligent" P and PD controllers are employed for the longitudinal and lateral motions of a vehicle. This new approach has been developed and used in order to ensure simultaneously a best profile tracking for the longitudinal and lateral behaviors. The longitudinal speed and the derivative of the lat...

The objective of this paper is to design a new integrated methodology for the detection of a critical situation in vehicle longitudinal dynamics. In classical modern vehicle, the ABS - anti-lock braking system - (during bracking) and anti-skid (during accelerations) modules are acting separately. This paper presents an innovative methodology for th...

In this work, a Continuous-Time Switched H∞ Proportional-Integral (CTSH∞PI) observer is presented. The estimation method is based on a proportional-integral observer introduced by [13], [11], [12]. The estimation method is used to estimate simultaneously the state variables and unknown inputs of switched systems. A design method is established usin...

This paper presents the INOVE “Integrated approach for observation and control of vehicle dynamics” project. The aim and organization of the project are described and we present some recent results on the proposed integrated approach to design new methodologies for the improvement of the vehicle dynamical behaviour.

This paper addresses an integration of two advanced vehicle controllers. The first one is developed for coupled control of longitudinal and lateral vehicle's motions. It takes advantage of differential flatness of nonlinear systems and algebraic identification techniques for denoising and numerical differentiation. The second one is an LPV/ℋ∞ contr...

This paper addresses the issue of the exponential stability of hybrid hyperbolic systems with switching boundary conditions. Our contribution is to show, through the specific example of SMB chromatography, how exponential stability (in L2-norm) can be established when the switching mechanism is precisely defined. The obtained stability conditions a...

Over the past decade, a lot of researches have been done on the development of advanced driver assistance systems (ADAS). Most of these ADAS are now active and need to be tested and evaluated before large deployment. In these ADAS, the prototyping and the implementation of the control stages are risky stages and not so easy to carry out. Indeed, th...

A combined nonlinear longitudinal and lateral vehicle control is investigated. Flatness-based nonlinear control and new algebraic estimation techniques for noise removal and numerical differentiation are the main theoretical tools. An accurate automatic path-tracking via vehicle steering angle and driving/braking wheel torque is thus ensured. It co...

In this paper, the problem of the switched H∞ tracking output feedback control problem is studied. The control design problem is addressed in the context of discrete-time switched linear systems. Then, the design of continuous-time case becomes trivial. Linear Matrix Inequality (LMI) and Linear Matrix Equality (LME) representations are used to expr...

The newly introduced model-free control is applied to a multivariable decoupled longitudinal and lateral vehicle control. It combines two outputs (lateral and longitudinal motions) via two inputs (braking/traction wheel torques and steering angle). It yields driving maneuvers requiring a control coordination of steering angle, braking and traction...

This paper presents a new LPV/H∞ semi-active suspension control strategy for a commercial vehicle equipped with 4 Magneto-Rheological dampers. The proposed approach concerns road adaptation using on-line road profile identification based on a non linear algebraic observer with unknown input. Then, the suspensions forces distribution in each corner...

Two control laws for switched uncertain linear systems are proposed: firstly, a continuous-time switched H∞ state feedback control is given, and secondly, a discrete-time H∞ state feedback control. These controllers are designed using a common Lyapunov function approach and switched Lyapunov function approach used for switched continuous-time and s...

This paper proposes a study and a comparison between two efficient and relatively recent vehicle control dynamics strategies, namely, the non linear Flatness control strategy and the LPV/H∞ control strategy. The first one concerns a controller based on the differential algebraic flatness of non linear systems and an algebraic non linear estimation...

The estimation problem of the road bank angle and the roll vehicle angle is presented in this work. These angles play an important role for the vehicle stability and the Vehicle Dynamic Control (VDC). However, the estimation of these angles requires a global vehicle model; unfortunately, the requirements related to the knowledge of the vehicle mode...

Simulation has been widely used to estimate the benefits of Cooperative Systems (CS) based on Inter-Vehicular Communications (IVC). This paper presents a new architecture built with the SiVIC simulator and the RTMaps™ multisensors prototyping platform. We introduce several improvements from a previous similar architecture, regarding IVC modelisatio...

Résumé. On présente une commande non linéaire couplée des modes longitudinal et latéral d'un véhicule et un estimateur du dévers de la route. Platitude différentielle dessys emes non linéaires et techniques algébriques d'estimation en sont les ingrédients théoriques principaux. Abstract. This paper deals with a coupled longitudinal/lateral vehicle...

Brigitte d'Andréa-Novel, professeur d'automatique à MINES ParisTech, a coordonné cet ouvrage. Il est le fruit de l'expérience du cours intitulé " Acoustique, Informatique, MusiquE " qu'elle a créé pour les élèves ingénieurs de troisième année du cycle ingénieurs civils. Son objectif est de présenter un très large panorama des outils scientifiques d...

A combined longitudinal and lateral vehicle control is presented. It employs flatness-based control and new algebraic estimation techniques for the numerical differentiation of noisy signals. This nonlinear control is designed for automatic path-tracking via vehicle steering angle and driving/braking wheel torque. It combines the control of the lat...

This paper deals with path planning and the associated control for a car-like vehicle in parallel parking problem. Our path planning method is purely based on a geometric approach such as minimal turning radii, which can be determined by the geometry of a vehicle and its maximum steering angle. The main strategy for parallel parking comes from retr...

A new approach to estimate vehicle tire forces and road maximum adherence is presented. Contrarily to most of previous works on this subject, it is not an asymptotic observer based estimation, but a combination of elementary diagnosis tools and new algebraic techniques for filtering and estimating derivatives of noisy signals. In a first step, inst...

It is obvious to say that perception is necessary to drive. Futhermore we can say that a good visibility is a guaranty for passengers security. The driver will adapt the vehicle speed to the offered visibility. Strong visibility reductions (dense fog for instance) are conditions of risk of accident. We therefore propose here a method to perform an...

A new approach to estimate the road maximum adherence is presented. It is based on a combination of new algebraic tools for estimation and diagnosis via numerical differentiation of noisy signals. Instantaneous friction is first computed within this framework. Then, extended braking stiffness concept is exploited to detect which braking efforts all...

The ubiquity of PID controllers in the industry has remained mysterious until now. We provide here a mathematical explanation of this strange phenomenon by comparing their sampling with the the one of “intelligent” PID controllers, which were recently introduced. Some computer simulations nevertheless confirm the superiority of the new intelligent...

In this paper, we consider the problem of modeling and control of a slide flute: a kind of recorder without finger holes but which is ended by a piston mechanism to modify the length of the resonator. A previous study has been done (see [1]), but with a very simple boundary condition for the mouth, corresponding to an ideal situation assuming that...

In this paper, a simplified model of a brass instrument is introduced. It is composed of a valve (including the mechanics of the lips), a jet (coupled with the valve dynamics), and a straight acoustic pipe excited by the jet, radiating in the air, and with frequency independent losses. This model couples an ordinary differential equation (valve) to...

We present for the longitudinal control of an electrical vehicle a "model-free'' control strategy, which is illustrated by convincing experimental results. The physical control is a coefficient rate of the maximal voltage of the battery. The chassis and the engine dynamical equations exhibit complex unknown parameters and/or neglected terms. The pr...

The ubiquity of PID controllers in the industry has remained mysterious until now. We provide here a mathematical explanation of this strange phenomenon by comparing their sampling with the the one of "intelligent" PID controllers, which were recently introduced. Some computer simulations nevertheless confirm the superiority of the new intelligent...

This communication is devoted to the performance evaluation of new numerical differentiators, of algebraic flavor, which lead to the solution of many pending questions in control, signal and finance. The continuous-time expression of such a differentiator is an integral over a short time window of the signal multiplied by some polynomial time funct...

In this paper we propose a complete strategy for the longitudinal control of automotive vehicles in Stop-and- Go situations. Firstly, a upper level grey-box torque control is proposed to compensate for neglected dynamics at chassis level (due for example to road slopes, aerodynamic forces, rolling resistance forces, etc.). Secondly, to obtain the d...

In this paper we propose a complete strategy for the longitudinal control of automotive vehicles in Stop-and- Go situations. Firstly, a upper level grey-box torque control is proposed to compensate for neglected dynamics at chassis level (due for example to road slopes, aerodynamic forces, rolling resistance forces, etc.). Secondly, to obtain the d...

We address the issue of the exponential stability (in L2-norm) of the classical solutions of the linearised Saint-Venant equations for a sloping channel. We give an explicit sucient dissipative condition which guarantees the exponential stability under subcritical flow conditions without additional assumptions on the size of the bottom and friction...

This paper describes a robust stop-and-go control strategy for vehicles. Since sensors used in a real automotive context are generally low cost, measurements are quite noisy. Furthermore, many vehicle/road interaction factors (road slope, rolling resistance, aerodynamic forces) are very poorly known. Hence, a robust strategy to noise and parameters...

This paper presents a robust stop-and-go control law, especially well adapted to car following scenarios in urban environments. Since many vehicle/road interaction factors (road slope, rolling resistance, aerodynamic forces) are very poorly known and measurements are quite noisy, a robust strategy is proposed within an algebraic framework. On the o...

In this paper wind instruments are modeled as time delay systems. In fact, a wind instrument is usually made of a linear acoustic resonator (the pipe) coupled with a nonlinear oscillator (the mouth of the instrument). The resonator can be modeled through hyperbolic wave equations. Two kinds of instruments are considered : the first one is a slide f...

In this paper, a modal analysis is performed for the slide flute modeled in d'AndréaN et al. (2009) using the linearized boundary conditions which can also be used to compute the suitable blowing pressure (linked to the mouth delay) and the suitable pipe length (linked to the pipe delay) to obtain a desired fundamental frequency or equivalently a d...

On analyse les performance de dérivateurs numériques récents, de nature algébrique, qui ont permis de résoudre bien des questions en automatique, signal et finance. La discrétisation d'un tel dérivateur, qui s'exprime en temps continu comme une intégrale, sur une courte fenêtre de temps, du signal multiplié par un certain polynôme temporel, est un...

Sufficient dissipative boundary conditions are given for the exponential stability of equilibria in physical networks of 2 × 2 nonlinear hyperbolic balance laws under boundary feedback control. The analysis relies on the use of an explicit strict Lyapunov function.

The presence of an area with low visibility conditions is a relevant information for autonomous vehicle as far as environment sensing is important regarding safety. In this aim, we develop a generic sensor of visibility using an onboard camera in a vehicle. Our approach consists in estimating the range to the most distant object belonging to the pl...

In this paper, we consider the problem of modeling and control of a slide flute : a kind of recorder without finger holes but which is ended by a piston mechanism to modify the length of the resonator (see Fig. 1). A previous study has been done (see (d'Andrea-Novel et al., 2007)), but with a very simple boundary condition for the mouth, correspond...

This paper presents a new approach for estimating vehicle velocities at its gravity center. The proposed strategy relies on recent algebraic techniques for numerical differentiation and diagnosis. We do not use any tire model in order to obtain an estimation, which is robust with respect to model uncertainties (friction, ...). All available measure...

The aim of this talk is to present some classical techniques and methods from control theory to deal with the problem of sound synthesis based on physical models. A first part will be devoted to the case of finite-dimensional state space, illustrated by: 1. Kelly-Lochbaum structure for 1D wave equations; 2. Realization theory for passive impedance...

In this paper, we consider the problem of modeling and control of a slide flute: a kind of recorder without finger holes but which is ended by a piston mechanism to modify the length of the resonator. A previous study has been done, but with a very simple boundary condition for the mouth, corresponding to an ideal situation assuming that the acoust...

We consider a simplified model of a trumpet-like instrument composed of a valve (including the mechanics of the lips), a jet (coupled with the valve dynamics), and an acoustic pipe excited by the jet and radiating in the air. A special care is devoted to the energy balance of the whole system and its dissipative property. This leads us to introduce...

A strict Lyapunov function for boundary control with integral actions of hyperbolic systems of conservation laws that can be diagonalised with Riemann invariants, is presented. The time derivative of this Lyapunov function can be made strictly negative definite by an appropriate choice of the boundary conditions and the integral control gains. Prev...

We give a new sufficient condition on the boundary conditions for the exponential stability of one-dimensional nonlinear hyperbolic systems on a bounded interval. Our proof relies on the construction of an explicit strict Lyapunov function. We compare our sufficient condition with other known sufficient conditions for nonlinear and linear one-dimen...

In this paper, we propose a robust algebraic approach to deal with noisy signal from radar in the context of Stop-and-Go scenarios which need inter-distance measurements for the control law. In general, commercial radars for cars are of such low quality that the measured signal is very noisy and the performance is not good enough to be used directl...

Cet article présente une nouvelle approche pour l'estimation des vitesses au centre de gravité d'un véhicule. Dans le but d'obtenir une estimation la plus robuste possible vis à vis de variations paramétriques et notamment de l'adhérence, nous utilisons les mesures disponibles dans un véhicule de série, sans chercher à modéliser les efforts pneumat...

The presence of an area with low visibility conditions is a relevant information to communicate to drivers before they reach this area. In this aim, we develop a generic sensor of visibility using an onboard camera in a vehicle equipped with vehicle-to-infrastructure (V2I) communications. Our approach consists in estimating the range to the most di...

It is shown how an entropy-based Lyapunov function can be used for the stability analysis of equilibria in networks of scalar conservation laws. The analysis gives a sucient stability condition which is weaker than the condition which was previously known in the literature. Various extensions and generalisations are briefly discussed. The approach...

This paper presents a feedback steering control strategy for a vehicle in an automatic driving context. Two main contributions in terms of control are highlighted. On the one hand, the automatic reference trajectories generation from geometric path constraints (obstacles). Thanks to the flatness property of the considered model, the longitudinal ve...

We present a strict Lyapunov function for hyperbolic systems of conservation laws that can be diagonalized with Riemann invariants. The time derivative of this Lyapunov function can be made strictly negative definite by an appropriate choice of the boundary conditions. It is shown that the derived boundary control allows to guarantee the local conv...

The dynamics of non holonomic mechanical system are described by the classical Euler-Lagrange equations subjected to a set of non-integrable constraints. Non holonomic systems are strongly accessible whatever the structure of the constraints. They cannot be asymptotically stabilized by a smooth pure state feedback. However smooth state feedback con...

We propose a boundary control methodology based on Riemann invariants to control the state of an hyperbolic system of conservation laws at a boundary, when a known disturbance is applied at the other boundary. The resulting control is an explicit feedforward expression, function of the disturbance at past time instants. The method is illustrated wi...

We present a strict Lyapunov function for hyperbolic systems of conservation laws that can be diagonalised with Riemann invariants. The time derivative of this Lyapunov function can be made strictly definite negative by an appropriate choice of the boundary conditions. It is shown that the derived boundary control allows to guarantee the local conv...

This article deals with the regulation of water flow in open-channels modelled by Saint-Venant equations. By means of a Riemann invariants approach, we deduce stabilizing control laws for a single horizontal reach without friction. The stability condition is extended to a general class of hyperbolic systems which can describe canal networks with mo...

The paper deals with the stabilization of distributed hyperbolic systems. It describes a generic method for building Lyapunov function candidates based on entropies. The method is illustrated with a case-study.

This paper deals with the uniform exponential stabilization of a hybrid PDE–ODE system which describes an overhead crane with flexible cable. A previous linear boundary feedback law (see d'Andréa-Novel, Boustany, Conrad & Rao (1994). MCSS Journal, 1, 1–22) depending on the platform position and velocity and on the angular displacement of the cable...

This paper deals with the stabilization of a rotating body-beam system with torque control. The system we consider is the one studied by Baillieul and Levi (1987). Xu and Baillieul proved (1993) that, for any constant angular velocity smaller than a critical one, this system can be stabilized by means of a feedback torque control law if there is da...

The goal of this paper is to propose observer-based controllers, either in state-space form or in polynomial representation, for fractional differential systems. As for linear differential systems of integer order, polynomial representation will allow us to take advantage of the Youla parametrization in order to asymptotically reject some perturbat...

This paper concerns the joystick control of the the high performance econo vehicle developed by Mitsubishi Heavy Industries featuring 2 independent fully actuated steering wheels. For this purpose, we propose a velocity control law based on the assumption of pure rolling without slipping wheel/road contact and the techniques of dynamic feedback lin...