We introduce flat systems, which are equivalent to linear ones via a special type of feedback called endogenous. Their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of Kalman's controllability. The distance to flatness is measured by a non-negative integer, the defect. We utilize differential algebra where flatness- and defect are best defined without distinguishing between input, state, output and other variables. Many realistic classes of examples are flat. We treat two popular ones: the crane and the car with n trailers, the motion planning of which is obtained via elementary properties of plane curves. The three non-flat examples, the simple, double and variable length pendulums, are borrowed from non-linear physics. A high frequency control strategy is proposed such that the averaged systems become flat.

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Flatness and defect of non-linear systems: introductory theory and examples

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

This manuscript describes a unique class of locomotive robot: A soft robot, composed exclusively of soft materials (elastomeric polymers), which is inspired by animals (e.g., squid, starfish, worms) that do not have hard internal skeletons. Soft lithography was used to fabricate a pneumatically actuated robot capable of sophisticated locomotion (e.g., fluid movement of limbs and multiple gaits). This robot is quadrupedal; it uses no sensors, only five actuators, and a simple pneumatic valving system that operates at low pressures (< 10 psi). A combination of crawling and undulation gaits allowed this robot to navigate a difficult obstacle. This demonstration illustrates an advantage of soft robotics: They are systems in which simple types of actuation produce complex motion.

Multigait soft robot

Self-driving vehicles are a maturing technology with the potential to reshape mobility by enhancing the safety, accessibility, efficiency, and convenience of automotive transportation. Safety-critical tasks that must be executed by a self-driving vehicle include planning of motions through a dynamic environment shared with other vehicles and pedestrians, and their robust executions via feedback control. The objective of this paper is to survey the current state of the art on planning and control algorithms with particular regard to the urban setting. A selection of proposed techniques is reviewed along with a discussion of their effectiveness. The surveyed approaches differ in the vehicle mobility model used, in assumptions on the structure of the environment, and in computational requirements. The side by side comparison presented in this survey helps to gain insight into the strengths and limitations of the reviewed approaches and assists with system level design choices.

A Survey of Motion Planning and Control Techniques for Self-Driving Urban Vehicles

Provides a summary of recent developments in control of nonholonomic systems. The published literature has grown enormously during the last six years, and it is now possible to give a tutorial presentation of many of these developments. The objective of this article is to provide a unified and accessible presentation, placing the various models, problem formulations, approaches, and results into a proper context. It is hoped that this overview will provide a good introduction to the subject for nonspecialists in the field, while perhaps providing specialists with a better perspective of the field as a whole. The paper is organized as follows: introduction to nonholonomic control systems and where they arise in applications, classification of models of nonholonomic control systems, control problem formulations, motion planning results, stabilization results, and current and future research topics.

Developments in nonholonomic control problems

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 model are difficult to satisfy, this is due to the uncertainties which affect the parameters of the vehicle model, for example, the longitudinal speed that changes the values of the vehicle model parameters, the front and rear cornering stiffnesses. In order to overcome all these constraints on the knowledge of the vehicle model, a switched proportional integral H∞ observer is proposed. This observer is designed using non-increasing condition applied on the Lyapunov functions. Sufficient conditions of global convergence of this observer are presented and proved. All these conditions are expressed in term of the linear matrix inequality (LMI). An experimental validation shows the ability of the SPIH∞ observer to estimate simultaneously the banking angle and vehicle dynamics parameters.

Functional switched H ∞ Proportional Integral observer applied for road bank and vehicle roll angles estimation

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 stability. Several convincing computer simulations are displayed and discussed. Overshoots become therefore smaller. The driving comfort is increased and the robustness to time-delays is improved.

Finite-Time Stabilization of Longitudinal Control for Autonomous Vehicles via a Model-Free Approach

Center Manifold Theory for Stabilizing a Flexmle Mechanical System with a Pitchfork Bifurcation

Sur le contrˆole fronti`ere d’une ﬂˆute `a coulisse par fonction de Lyapunov Brigitte d’Andr´ea-Novel1 , Jean-Michel Coron2 , Georges Bastin 3 1 Centre de Robotique ´Ecole des Mines de Paris, 60, bld Saint Michel, 75272 Paris Cedex 06, France 2 D´epartement de Math´ematiques Universit´e de Paris-Sud, Bˆatiment 425, 91405 Orsay, France 3 CESAME Universit´e Catholique de Louvain, 4 avenue G. Lemaˆitre, 1348 Louvain-La-Neuve, Belgique R´esum´e— L’objet de ce papier concerne le contrˆole `a la fronti`ere d’une ﬂˆute munie d’un dispositif de coulisse per- mettant d’obtenir des notes de consigne en faisant varier la longueur du tuyau. Apr`es une mod´elisation du syst`eme par des ´Equations aux D´eriv´ees Partielles hyperboliques met- tant en oeuvre les variables de surpression acoustique et de d´ebit d’air dans le tuyau, le contrˆole fronti`ere de la coulisse est ´elabor´e `a partir d’une fonction de Lyapunov ad´equate exprim´ee `a partir des invariants de Riemann du syst`eme. I. Introduction Nous avons par le pass´e, ´etudi´e le contrˆole fronti`ere de syst`emes hyperboliques de lois de conservation par inva- riants de Riemann et/ou fon

Sur le contrôle frontière d’une ﬂûte à coulisse par fonction de Lyapunov

Systems control theory is a far developped field which helps to study stability, estimation and control of dynamical systems. The physical behaviour of musical instruments, once described by dynamical systems, can then be controlled and numerically simulated for many purposes. 
The aim of this paper is twofold: first, to provide the theoretical background on linear system theory, both in continuous and discrete time, mainly in the case of a finite number of degrees of freedom ; second, to give illustrative examples on wind instruments, such as the vocal tract represented as a waveguide, and a sliding flute.

Brigitte d'Andréa-Novel

Papers

Functional switched H ∞ Proportional Integral observer applied for road bank and vehicle roll angles estimation

Finite-Time Stabilization of Longitudinal Control for Autonomous Vehicles via a Model-Free Approach

Center Manifold Theory for Stabilizing a Flexmle Mechanical System with a Pitchfork Bifurcation

Sur le contrôle frontière d’une ﬂûte à coulisse par fonction de Lyapunov

Systems control theory applied to natural and synthetic musical sounds