Les avancées dans les technologies ont permis le développement de systèmes d’aide à la conduite (ADAS) pour prévenir les accidents routiers causés par les erreurs de conduite au manque d’attention de conducteurs. Plusieurs types sont déjà disponibles sur le marché, comme l’ABS et l’ESC (ou ESP), utilisant uniquement des capteurs proprioceptifs. Les capteurs extéroceptifs sont présents dans les ADAS plus récents, comme LKAS (maintien dans la voie) et LDWS. Cependant, l‘ESC agit dans la dynamique du véhicule en situations d¹urgence alors que les systèmes d’alerte de sortie de voie sont conçus pour les situations de faible sollicitation latérale. Cette thèse traite le développement d’un ADAS, nommé ESC-perceptif, qui intègre les informations des capteurs extéroceptifs (camera vidéo) avec le contrôle de la vitesse de lacet afin d’éviter les sorties de voie, y compris pour des conditions de fortes sollicitations latérales. La prise en compte de la saturation de forces de contact pneumatiques-chaussée est essentielle pour la conception de ce système. La non-linéairité des efforts pneumatiques est traité par l'approche des systèmes affines par morceaux (PWA). Cela permet de mener l'analyse et la synthèse de contrôleurs en combinant les fonctions de Lyapunov avec la résolution de problèmes d’optimisations sous contraintes d¹inégalités matricielles linéaires et bilinéaires. Au long de la thèse, plusieurs contrôleurs PWA pour le développement de ADAS sont présentés. L’ESC-perceptif, basé uniquement sur les capteurs disponibles sur les véhicules commercialisés est validé expérimentalement sur véhicule prototype. / Advances in the technology of sensors and actuators have enabled the development of driver assistance systems (ADAS) to prevent road accidents due to drivers mistakes or inattention. Several types are already deployed in the commercialised vehicles, such as, ABS and ESC by means of proprioceptive sensors. Exteroceptive sensors can be seen in systems such as, LKAS (Lane Keeping Assistance Systems) and LDWS (Lane Departure Warning Systems). While the ESC deals with the vehicle dynamics in emergency situations, the systems to avoid lane departure are currently designed to work in conditions of weak lateral solicitation. This thesis deals with the development of a ADAS, named perceptive-ESC, which integrates the information from the exteroceptive sensors (provided by a video camera) with the yaw rate control in order to avoid unintended lane departure even in situation of strong lateral solicitation or degraded road adhesion. Considering the saturation of the lateral tyre forces is essential for the conception of the perceptive-ESC, therefore the nonlinear behaviour of the lateral tyre forces is taken into account by the use of Piecewise Affine (PWA) Systems which analysis and control synthesis are based on quadratic Lyapunov functions casted as optimisation problems with linear and bilinear matrix inequalities constraints. Throughout the thesis, several PWA controllers for driver assistance systems are presented in which the complexity is gradually increased from simply enhancing the vehicle handling to the perceptive-ESC based only on sensors available in the currently commercialised passenger cars, which has been validated by practical experiments on a prototype vehicle.

The (nonlinear) response behavior of a piecewise-linear system is investigated under both deterministic and stochastic excitations in this study. A semi-analytical procedure is developed to predict the system behavior by evaluating the joint probability density functions of the Fokker-Planck equations of the stochastic piecewise-linear system under random excitations via a path-integral solution procedure. From an analysis of the deterministic system, nonlinear system behavior is derived for further analysis of the corresponding stochastic system. The influence of variations in other parameters on the response behavior are also examined. In the stochastic system analysis, which represents a more realistic approach to understanding the system behavior, a Markov process approach is used. By introducing random perturbations in the harmonic excitation, the stochastic responses are examined and compared to those of the corresponding deterministic system. Stability of the various responses including regular and chaotic motions, is investigated by varying the noise intensity. Routes to chaos in period-doubling processes with and without external random perturbations are studied and compared. Stationarity and ergodicity of the chaotic responses of the system are examined via time domain and probability domain simulations. Potential coexisting responses of the piecewise-linear system are examined via the path-integral solutions. It is found that the path-integral solutions can provide global information of the system behavior in the probability domain, and can also verify the potential coexisting responses and discern the relative strength of the coexisting response attractors. / Graduation date: 1996

No description available.

Thesis (Ph. D.)--School of Industrial and Systems Engineering, Georgia Institute of Technology, 2004. Directed by George L. Nemhauser. / Vita. Includes bibliographical references (leaves 91-94).

No description available.

It is well known that in many areas of computational mathematics, wavelet based algorithms are becoming popular for modeling and analyzing data and for providing efficient means for hierarchical data decomposition of function spaces into mutually orthogonal wavelet spaces. Wavelet construction in more than one-dimensional setting is a very challenging and important research topic. In this thesis, we first introduce the method of construction wavelets by using semi-wavelets. Second, we construct piecewise linear wavelets with smaller support over type-2 triangulations. Then, parameterized wavelets are constructed using the orthogonality conditions.

No description available.

Piecewise-smooth stochastic systems are widely used in engineering science. However, the theory of these systems is only in its infancy. In this thesis, we take as an example the Brownian motion with dry friction to illustrate dynamical properties of these systems with respect to three interesting topics: (i) weak-noise approximations, (ii) first-passage time (FPT) problems and (iii) functionals of stochastic processes. Firstly, we investigate the validity and accuracy of weak-noise approximations for piecewise-smooth stochastic differential equations (SDEs), taking as an illustrative example the Brownian motion with pure dry friction. For this model, we show that the weak-noise approximation of the path integral correctly reproduces the known propagator of the SDE at lowest order in the noise power, as well as the main features of the exact propagator with higher-order corrections, provided that the singularity of the path integral is treated with some heuristics. We also consider a smooth regularisation of this piecewise-constant SDE and study to what extent this regularisation can rectify some of the problems encountered in the non-smooth case. Secondly, we provide analytic solutions to the FPT problem of the Brownian motion with dry friction. For the pure dry friction case, we find a phase transition phenomenon in the spectrum which relates to the position of the exit point and affects the tail of the FPT distribution. For the model with dry and viscous friction, we evaluate quantitatively the impact of the corresponding stick-slip transition and of the transition to ballistic exit. We also derive analytically the distributions of the maximum velocity till the FPT for the dry friction model. Thirdly, we generalise the so-called backward Fokker-Planck technique and obtain a recursive ordinary differential equation for the moments of functionals in the Laplace space. We then apply the developed results to analyse the local time, the occupation time and the displacement of the dry friction model. Finally, we conclude this thesis and state some related unsolved problems.

<p>En gren inom statistikteorin är den så kallade Regressionsanalysen där man studerar hur data från exempelvis ett stickprov kan anpassas till en graf. Skrivandet av denna uppsats har haft som syfte att studera några av de metoder som finns att tillgå vid bestämning av de ingående parametrarna i de enklare fallen av regression. Dessutom ges i de avslutande kapitlen exempel på den del inom regressionsanalysen som kallas Styckvis Linjär Regression eller <em>Piecewise Linear Regression.</em></p> / Presentationen är redan avklarad den 26 april 2010 kl. 11.30

We study a generic minimization problem with separable non-convex piecewise linear costs, showing that the linear programming (LP) relaxation of three textbook mixed integer programming formulations each approximates the cost function by its lower convex envelope. We also show a relationship between this result and classical Lagrangian duality theory.