Global ETD Search

11	Optimal control and stability of four-wheeled vehicles Masouleh, Mehdi Imani January 2017 (has links) Two vehicular optimal control problems are visited. The first relates to the minimum lap time problem, which is of interest in racing and the second the minimum fuel problem, which is of great importance in commercial road vehicles. Historically, minimum lap time problems were considered impractical due to their slow solution times compared with the quasi-steady static (QSS) simulations. However, with increasing computational power and advancement of numerical algorithms, such problems have become an invaluable tool for the racing teams. To keep the solution times reasonable, much attention still has to be paid to the problem formulation. The suspension of a Formula One car is modelled using classical mechanics and a meta-model is proposed to enable its incorporation in the optimal control problem. The interactions between the aerodynamics and the suspension are thereby studied and various related parameters are optimised. Aerodynamics plays a crucial role in the performance of Formula One cars. The influence of a locally applied perturbation to the aerodynamic balance is investigated to determine if a compromise made in design can actually lead to lap time improvements. Various issues related to minimum lap time calculations are then discussed. With the danger of climate change and the pressing need to reduce emissions, improvements in fuel consumption are presently needed more than ever. A methodology is developed for fuel performance optimisation of a hybrid vehicle equipped with an undersized engine, battery and a flywheel. Rather than using the widely used driving cycles, a three-dimensional route is chosen and the optimal driving and power management strategy is found with respect to a time of arrival constraint. The benefits of a multi-storage configuration are thereby demonstrated. Finally, the nonlinear stability of a vehicle model described by rational vector fields is investigated using region of attraction (RoA) analysis. With the aid of sum-of-squares programming techniques, Lyapunov functions are found whose level sets act as an under-approximation to the RoA. The influence of different vehicle parameters and driving conditions on the RoA is studied.
12	Systèmes quasi-LPV continus : comment dépasser le cadre du quadratique ? / Continuous quasi-LPV Systems : how to leave the quadratic framework? Jaadari, Abdelhafidh 03 July 2013 (has links) Cette thèse aborde le problème de l'analyse de la stabilité et de la conception des lois de commande pour les systèmes non linéaires mis sous la forme de modèles flous continus de type Takagi-Sugeno. L'analyse de stabilité est généralement basée sur la méthode directe de Lyapunov. Plusieurs approches existent dans la littérature, basées sur des fonctions de Lyapunov quadratiques sont proposées pour résoudre ce problème, les résultats obtenus à l'aide des telles fonctions introduisent un conservatisme qui peut être très préjudiciable. Pour surmonter ce problème, différentes approches basées sur des fonctions de Lyapunov non quadratiques ont été proposées, néanmoins ces approches sont basées sur desconditions très restrictives. L'idée développée dans ce travail est d'utiliser des fonctions de Lyapunov non quadratiques et des contrôleurs non-PDC afin d'en tirer des conditions de stabilité et de stabilisation moins conservatives. Les propositions principales sont : l'utilisation des bornes locales des dérivées partielles au lieu des dérivés des fonctions d’appartenances, le découplage du gain du régulateur des variables de décision de la fonction Lyapunov, l’utilisation des fonctions de Lyapunov floues polynomiales dans l’environnement des polynômes et la proposition de la synthèse de contrôleur vérifiant certaines limites de dérivés respectées dans une région de la modélisation à la place de les vérifier a posteriori. Ces nouvelles approches permettent de proposer des conditions locales afin de stabiliser les modèles flous continus de type T-S, y compris ceux qui n'admettent pas une stabilisation quadratique et obtenir des domaines de stabilité plus grand. Plusieurs exemples de simulation sont choisis afin de vérifier les résultats présentésdans cette thèse. / This thesis deals with the problem of stability analysis and control design for nonlinear systems in the form of continuous-time Takagi-Sugeno models. The approach to stability analysis is usually based on the direct Lyapunov method. Several approaches in the literature, based on quadratic Lyapunov functions, are proposed to solve this problem ; the results obtained using such functions introduce a conservatism that can be very detrimental. To overcome this problem, various approaches based on non-quadratic Lyapunov functions have also been recently presented; however, these approaches are based on very conservative bounds or too restrictive conditions. The idea developed in this work is to use non-quadratic Lyapunov functions and non-PDC controller in order to derive less conservative stability and stabilization conditions. The main proposals are : using local bounds in partial derivatives instead of time derivatives of the memberships,decoupling the controller gain from the Lyapunov function decision variables, using fuzzy Lyapunov functions in polynomial settings and proposing the synthesis of controller ensuring a priori known time-derivative bounds are fulfilled in a modelling region instead of checking them a posteriori. These new approaches allow proposing local conditions to stabilize continuous T-S fuzzy systems including those that do not admit a quadratic stabilization. Several simulation examples are chosen to verify the results given in this dissertation. Modèles flous de types Takagi-Sugeno Stabilité non-quadratique Stabilisationnon-quadratique Fonction de Lyapunov Inégalités matricielle linéaires Somme descarrées Takagi-Sugeno Models Non-quadratic Stability Non-quadratic Stabilization Lyapunov function Linear Matrix inqualities Sum Of Squares
13	Simulation and Control at the Boundaries Between Humans and Assistive Robots Warner, Holly E. January 2019 (has links) No description available. Biomechanics Biomedical Engineering Engineering Mechanical Engineering Robotics Robots Prosthesis Transfemoral Above-knee Powered Energy regeneration Gait emulator Human-machine interaction Musculoskeletal model Sum of squares polynomial Differential flatness Exercise Control Impedance Backstepping Optimal Model predictive
14	Contribution à la commande de systèmes non linéaires sous échantillonnage apériodique / Contribution to the control of nonlinear systems under aperiodic sampling Omran, Hassan 24 March 2014 (has links) Cette thèse est dédiée à l’analyse de stabilité des systèmes non linéaires sous échantillonnage variant avec le temps. Lors de l’implémentation numérique d’un contrôleur qui est calculé en temps-continu (approche par émulation), il est d'un grand intérêt de fournir des critères de stabilité et d’estimer la borne supérieure de l’intervalle d’échantillonnage qui garantit la stabilité du système en temps discret. Plusieurs travaux récents ont abordé ces questions dans le cas de modèles linéaires, mais la question a rarement été abordée dans une étude quantitative et formelle pour les systèmes non linéaires.Tout d'abord, le mémoire présente un aperçu sur les systèmes échantillonnés. Les défis et les principales méthodes pour l'analyse de stabilité sont présentés pour le cas des systèmes linéaires invariants dans le temps et celui des systèmes non linéaires. Ensuite, l’analyse de la stabilité locale des systèmes bilinéaires échantillonnés contrôlés par un retour d'état linéaire est considérée. Deux approches sont utilisées, la première basée sur la théorie des systèmes hybrides, la seconde basée sur l’analyse des ensembles invariants contractants. Cette dernière approche est inspirée par la théorie de la dissipativité. L’ensemble de ces résultats conduisent à des conditions suffisantes de stabilité exprimées sous forme LMI.Enfin, les conditions de stabilité basées sur la dissipativité sont étendues au cas des systèmes non linéaires affines en l'entrée. Les résultats sont ensuite repris dans le cas spécifique des systèmes non linéaires polynomiaux où les conditions de stabilité sont vérifiées numériquement en utilisant la décomposition en somme des carrés (SOS). / This PhD thesis is dedicated to the stability analyzis of nonlinear systems under sampled-data control, with arbitrarily time-varying sampling intervals. When a controller is designed in continuous-time, and then implemented digitally (emulation approach), it is of great interest to provide stability criteria, and to estimate the bound on the sampling intervals which guarantees the stability of the sampled-data system. Whereas several works deal with linear models, the issue has been rarely addressed in a formal quantitative study in the nonlinear case.First, an overview on sampled-data control is presented. Challenges and main methodologies for stability analysis are presented for both the linear time-invariant and the nonlinear cases.Then, local stability of bilinear sampled-data systems controlled by a linear state feedback is considered by using two approaches: the first one is based on hybrid systems theory; the second one is based on the analyzis of contractive invariant sets and is inspired by the dissipativity theory. Both approaches provide sufficient stability conditions in the form of LMI.Finally, the dissipativity–based stability conditions are extended for the more general case of nonlinear systems which are affine in the input, including the case of polynomial systems which leads to conditions in the form of sum of squares (SOS). Systèmes échantillonnées Systèmes bilinéaires Systèmes non linéaires Systèmes dynamiquess hybrides Echantillonnage apériodique Stabilité Dissipativité Somme des carrés (SOS) Sampled -data systems Bilinear systems Nonlinear systems Hybrid dynamical systems Aperiodic sampling Stability Dissipativity Linear matrix inequalities (LMIs Sum of squares (SOS)
15	Contributions to analysis and control of Takagi-Sugeno systems via piecewise, parameter-dependent, and integral Lyapunov functions González Germán, Iván Temoatzin 04 May 2018 (has links) Esta tesis considera un enfoque basado en Lyapunov para el análisis y control de sistemas no lineales cuyas ecuaciones dinámicas son reescritas como un modelo Takagi-Sugeno o uno polinomial convexo. Estas estructuras permiten resolver problemas de control mediante técnicas de optimización convexa, más concretamente desigualdades matriciales lineales y suma de cuadrados, que son eficientes herramientas desde un punto de vista computacional. Después de proporcionar una visión general básica del estado actual en el campo de los modelos Takagi-Sugeno, esta tesis aborda cuestiones sobre las funciones de Lyapunov por trozos, dependiente de parámetros e integral de línea, con las siguientes contribuciones: Un algoritmo mejorado para estimaciones del dominio de atracción de sistemas no lineales para sistemas de tiempo continuo. Los resultados se basan en funciones de Lyapunov por trozos, desigualdades matriciales lineales y argumentaciones geométricas; enfoques basados en conjuntos de nivel en la literatura previa se han mejorado significativamente. Una función Lyapunov generalizada dependiente de parámetros para la síntesis de controladores para sistemas Takagi-Sugeno. El enfoque propone una ley de control multi-índice que retroalimenta la derivada del tiempo de las funciones de membresía del modelo Takagi-Sugeno para anular los términos que causan localidad a priori en el análisis de Lyapunov. Una nueva función integral de Lyapunov para el análisis de estabilidad de sistemas no lineales. Estos resultados generalizan aquellos basados en funciones de Lyapunov integral de línea al marco polinomial; resulta que los requisitos de independencia del camino pueden ser anulados por una definición adecuada de una función Lyapunov con términos integrales. / This thesis considers a Lyapunov-based approach for analysis and control of nonlinear systems whose dynamical equations are rewritten as a Takagi-Sugeno model or a convex polynomial one. These structures allow solving control problems via convex optimisation techniques, more specifically linear matrix inequalities and sum-of-squares, which are efficient tools from the computational point of view. After providing a basic overview of the state of the art in the field of Takagi-Sugeno models, this thesis address issues on piecewise, parameter-dependent and line-integral Lyapunov functions, with the following contributions: An improved algorithm to estimate the domain of attraction of nonlinear systems for continuous-time systems. The results are based on piecewise Lyapunov functions, linear matrix inequalities, and geometrical argumentations; level-set approaches in prior literature are significantly improved. A generalised parameter-dependent Lyapunov function for synthesis of controllers for Takagi-Sugeno systems. The approach proposed a multi-index control law that feeds back the time derivative of the membership function of the Takagi-Sugeno model to cancel out the terms that cause a priori locality in the Lyapunov analysis. A new integral Lyapunov function for stability analysis of nonlinear systems. These results generalise those based on line-integral Lyapunov functions to the polynomial framework; it turns out path-independency requirements can be overridden by an adequate definition of a Lyapunov function with integral terms. / Aquesta tesi considera un enfocament basat en Lyapunov per a l'anàlisi i control de sistemes no lineals les equacions dinàmiques dels quals són reescrites com un model Takagi-Sugeno o un de polinomial convex. Aquestes estructures permeten resoldre problemes de control mitjançant tècniques d'optimització convexa, més concretament desigualtats matricials lineals i suma de quadrats, que són eines eficients des d'un punt de vista computacional. Després de proporcionar una visió general bàsica de l'estat actual en el camp dels models Takagi-Sugeno, aquesta tesi aborda qüestions sobre les funcions de Lyapunov per trossos, dependent de paràmetres i integral de línia, amb les següents contribucions: Un algoritme millorat per a estimar el domini d'atracció de sistemes no lineals per a sistemes de temps continu. Els resultats es basen en funcions de Lyapunov per trossos, desigualtats matricials lineals i argumentacions geomètriques; enfocaments basats en conjunts de nivell en la literatura prèvia s'han millorat significativament. Una funció Lyapunov generalitzada dependent de paràmetres per a la síntesi de controladors per a sistemes Takagi-Sugeno. L'enfocament proposa una llei de control multi-índex que retroalimenta la derivada del temps de les funcions de membres del model Takagi-Sugeno per anul·lar els termes que causen localitat a priori en l'anàlisi de Lyapunov. Una nova funció integral de Lyapunov per a l'anàlisi d'estabilitat de sistemes no lineals. Aquests resultats generalitzen aquells basats en funcions de Lyapunov integral de línia al marc polinomial; resulta que els requisits d'independència del camí poden ser anul·lats per una definició adequada d'una funció Lyapunov amb termes integrals. / González Germán, IT. (2018). Contributions to analysis and control of Takagi-Sugeno systems via piecewise, parameter-dependent, and integral Lyapunov functions [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/101282 Nonlinear systems Takagi-Sugeno models Lyapunov function Linear matrix inequalities Sum-of-squares LPV Linear parameter-varying systems Piecewise Lyapunov function Stability nonlinear systems Stabilization nonlinear systems Polynomial Lyapunov function Parameter-dependent Lyapunov function Domain of attraction Semidefinite programming INGENIERIA DE SISTEMAS Y AUTOMATICA
16	Highway Development Decision-Making Under Uncertainty: Analysis, Critique and Advancement El-Khatib, Mayar January 2010 (has links) While decision-making under uncertainty is a major universal problem, its implications in the field of transportation systems are especially enormous; where the benefits of right decisions are tremendous, the consequences of wrong ones are potentially disastrous. In the realm of highway systems, decisions related to the highway configuration (number of lanes, right of way, etc.) need to incorporate both the traffic demand and land price uncertainties. In the literature, these uncertainties have generally been modeled using the Geometric Brownian Motion (GBM) process, which has been used extensively in modeling many other real life phenomena. But few scholars, including those who used the GBM in highway configuration decisions, have offered any rigorous justification for the use of this model. This thesis attempts to offer a detailed analysis of various aspects of transportation systems in relation to decision-making. It reveals some general insights as well as a new concept that extends the notion of opportunity cost to situations where wrong decisions could be made. Claiming deficiency of the GBM model, it also introduces a new formulation that utilizes a large and flexible parametric family of jump models (i.e., Lévy processes). To validate this claim, data related to traffic demand and land prices were collected and analyzed to reveal that their distributions, heavy-tailed and asymmetric, do not match well with the GBM model. As a remedy, this research used the Merton, Kou, and negative inverse Gaussian Lévy processes as possible alternatives. Though the results show indifference in relation to final decisions among the models, mathematically, they improve the precision of uncertainty models and the decision-making process. This furthers the quest for optimality in highway projects and beyond. highway development decision making under uncertainty real options jump processes infinitely divisible distributions Lévy processes measure theory characteristic function characteristic exponent Lévy jump measure probability measure cádlág stochastic process Wiener process Poisson process compound Poisson process finite activity models jump diffusion models Merton model Gaussian jump process Kou model double exponential jump process leptokurtic volatility smile infinite activity models pure jumps process generalized hyperbolic model modified Bessel function negative inverse Gaussian model geometric Brownian motion model log-normal distribution model normality assumption heavy-tailed distribution asymmetric distribution quantile-quantile plot Rydberg algorithm parameter calibration moments cummulants sum of squares Monte Carlo simulation least-squares regression backward dynamic programming discrete-time Markov chain land price traffic demand highway service quality index data collection traffic volume Annual Average Daily Traffic Ontario Ministry of Transportation Land Registry Office Freedom of Information Act seasonality value of transportation types of transportation systems importance of highway systems cost of wrong decisions monetary cost private sector cost human cost land expropriation environmental cost irreversibility cost factor time cost factor political cost factor opportunity cost opportunity cost of wrong decisions economic cost of wrong decisions economic cost of mis-estimation economic profit of wrong decisions cost of inaction price of making right decisions scope of decisions rehabilitation decision land acquisition decision expansion decision uncertainty modeling land acquisition cost expropriation cost construction cost material cost Montréal-Mirabel International Airport Pickering Airport 407 Express Toll Route Highway 407 Statistics
17	Highway Development Decision-Making Under Uncertainty: Analysis, Critique and Advancement El-Khatib, Mayar January 2010 (has links) While decision-making under uncertainty is a major universal problem, its implications in the field of transportation systems are especially enormous; where the benefits of right decisions are tremendous, the consequences of wrong ones are potentially disastrous. In the realm of highway systems, decisions related to the highway configuration (number of lanes, right of way, etc.) need to incorporate both the traffic demand and land price uncertainties. In the literature, these uncertainties have generally been modeled using the Geometric Brownian Motion (GBM) process, which has been used extensively in modeling many other real life phenomena. But few scholars, including those who used the GBM in highway configuration decisions, have offered any rigorous justification for the use of this model. This thesis attempts to offer a detailed analysis of various aspects of transportation systems in relation to decision-making. It reveals some general insights as well as a new concept that extends the notion of opportunity cost to situations where wrong decisions could be made. Claiming deficiency of the GBM model, it also introduces a new formulation that utilizes a large and flexible parametric family of jump models (i.e., Lévy processes). To validate this claim, data related to traffic demand and land prices were collected and analyzed to reveal that their distributions, heavy-tailed and asymmetric, do not match well with the GBM model. As a remedy, this research used the Merton, Kou, and negative inverse Gaussian Lévy processes as possible alternatives. Though the results show indifference in relation to final decisions among the models, mathematically, they improve the precision of uncertainty models and the decision-making process. This furthers the quest for optimality in highway projects and beyond. highway development decision making under uncertainty real options jump processes infinitely divisible distributions Lévy processes measure theory characteristic function characteristic exponent Lévy jump measure probability measure cádlág stochastic process Wiener process Poisson process compound Poisson process finite activity models jump diffusion models Merton model Gaussian jump process Kou model double exponential jump process leptokurtic volatility smile infinite activity models pure jumps process generalized hyperbolic model modified Bessel function negative inverse Gaussian model geometric Brownian motion model log-normal distribution model normality assumption heavy-tailed distribution asymmetric distribution quantile-quantile plot Rydberg algorithm parameter calibration moments cummulants sum of squares Monte Carlo simulation least-squares regression backward dynamic programming discrete-time Markov chain land price traffic demand highway service quality index data collection traffic volume Annual Average Daily Traffic Ontario Ministry of Transportation Land Registry Office Freedom of Information Act seasonality value of transportation types of transportation systems importance of highway systems cost of wrong decisions monetary cost private sector cost human cost land expropriation environmental cost irreversibility cost factor time cost factor political cost factor opportunity cost opportunity cost of wrong decisions economic cost of wrong decisions economic cost of mis-estimation economic profit of wrong decisions cost of inaction price of making right decisions scope of decisions rehabilitation decision land acquisition decision expansion decision uncertainty modeling land acquisition cost expropriation cost construction cost material cost Montréal-Mirabel International Airport Pickering Airport 407 Express Toll Route Highway 407 Statistics

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