Optimal Linear Parameter-Varying Control Design for a Pressurized Water Reactors

The applicability of employing parameter-dependent control to a nuclear pressurized water reactor is investigated. The synthesis techque produces a controller which achieves specified performance against the worst-case time variation of a measurable parameter which enters the plant in a linear fractional manner. The plant can thus have widely varying dynamics over the operating range. The results indicate this control technique is comparable to linear control when small operating ranges are considered

Linear Parameter-Varying Control of a Ducted Fan Engine

Parameter-dependent control techniques are applied to a vectored thrust, ducted fan engine. The synthesis technique is based on the solution of Linear Matrix Inequalities and produces a controller which achieves specified performance against the worst-case time variation of measurable parameters entering the plant in a linear fractional manner. Thus the plant can have widely varying dynamics over the operating range. The controller designed performs extremely well, and is compared to an ℋ∞ controller

An experimental comparison of controllers for a vectored thrust, ducted fan engine

Experimental comparisons between four different control design methodologies are applied to a small vectored thrust engine. Each controller is applied to three trajectories of varying aggressiveness. The control strategies considered are LQR, ℋ∞, gain scheduling, and feedback linearization. The experiments show that gain scheduling is essential to achieving good performance. The strengths and weaknesses of each methodology are also examined

Combining Dantzig-Wolfe and Benders decompositions to solve a large-scale nuclear outage planning problem

International audienceOptimizing nuclear unit outages is of significant economic importance for the French electricity company EDF, as these outages induce a substitute production by other more expensive means to fulfill electricity demand. This problem is quite challenging given the specific operating constraints of nuclear units, the stochasticity of both the demand and non-nuclear units availability, and the scale of the instances. To tackle these difficulties we use a combined decomposition approach. The operating constraints of the nuclear units are built into a Dantzig-Wolfe pricing subproblem whose solutions define the columns of a demand covering formulation. The scenarios of demand and non-nuclear units availability are handled in a Benders decomposition. Our approach is shown to scale up to the real-life instances of the French nuclear fleet

Contrôle de Systèmes Dynamiques Incertains et Résolution Exacte en Optimisation Combinatoire : Contributions et Applications

The contributions lie in two fields of applied mathematics, namely control of dynamicalsystems and combinatorial optimization. In control, the considered techniques are dedicated to a class of systems subject toeither linear time invariant (LTI) or linear parameter varying (LPV) structured uncertainty.The robust analysis under structured uncertainty is strongly NP-hard even in the LTI case.Convex optimization techniques lead to a conservative guarantee against the worst caseuncertainty. Multidimensional reduction techniques with guaranteed approximation errorbounds are proposed as a generalization of standard balanced truncature to reduce thesize of the uncertainty structure. They appear to be very helpful in the construction ofthe uncertain model, thus leading to less conservative results. The different techniquesare tested in applications coming from both aeronautics and energy either in lab experimentsor in an industrial context. In optimization, different aspects for the exact resolution of combinatorial problemsare considered, in particular complexity, feasibility, polyhedral analysis, symmetry,decomposition and data subject to uncertainty. The different problems investigated comefrom energy management and maintenance. The talk will focus on a selection of results, inparticular those relative to the complexity and polyhedral analysis of the Unit CommitmentProblem. A particular framework is also proposed to account for uncertainty in the spiritof the two stage setting used in robust optimization. The objective is to guarantee a subsetof decisions can be anchored, i.e., unchanged, between the two stages. The anchoringcriterium is to desensitize the solution to uncertainty in the same spirit as in robust control.Les contributions se situent dans deux domaines des mathématiques appliquées que sontl'automatique et l'optimisation. En automatique, des techniques de commande robuste applicables à une classe desystèmes présentant des incertitudes structurées sont considérées dans les cas linéaireà temps invariant (LTI) et linéaire à paramètres variants (LPV). Le problème d'analysede robustesse en stabilité vis à vis d'incertitudes structurées est NP-complet même dansle cas LTI. En se limitant à des techniques de résolution de problèmes convexes, lagarantie pour des incertitudes pire-cas bornées en norme dans une structure conduit àun conservatisme qui limite la taille de la structure pouvant être prise en compte pouratteindre un niveau de performance minimum demandé. Des techniques de réductionmultidimensionnelle avec erreur d'approximation garantie sont proposées commegénéralisation des techniques de troncature équilibrée. Elles se sont révélées êtreun élément déterminant dans la construction du modèle incertain pour réduire leconservatisme. Les différentes techniques étudiées ont fait l'objet d'applicationsdans le domaine de l'énergie et de l'aéronautique, aussi bien sur maquettes en laboqu'en contexte industriel. En optimisation, différents aspects de résolution exacte de problèmes d'optimisationcombinatoire ont été étudiés en fonction des problèmes étudiés tirés de problèmes réelsdans le domaine de l'énergie. Ils concernent la complexité, faisabilité, analysepolyédrale, symétries, décomposition et prise en compte d'aléa ou d'incertitude. Laprésentation portera sur une sélection de résultats, en particulier ceux relatifs àl'analyse de complexité et à l'analyse polyédrale du Unit Commitment Problem (UCP).Enfin, une problématique particulière est proposée pour étendre le cadre déterministede l'optimisation combinatoire en prenant en compte des données incertaines dans lalignée de ce qui est proposé en optimisation robuste à deux étapes. L'objectif est degarantir qu'un sous-ensemble de décisions peuvent être ancrées, i.e. inchangées, entreles deux étapes. L'idée de cette problématique d'ancrage est d'insensibiliser la solutionà l'incertitude. En ce sens cette problématique est commune à celle des techniques decommande robuste en automatique

An integer formulation based on common supersequences to solve the Permutation Problem using a Unit-Capacity Robot

International audienceGiven a finite sequence S over an alphabet, a sequence S’ is a supersequence of S if we can delete some characters in S’ such that the remaining sequence is equal to S. Given a finite set R of sequences, a common supersequence of R is a sequence which is a supersequence of every sequences of R. In this article, using a graph model introduced in [Bendotti et al 2013], we give a necessary and sufficient condition for the PPCR to be feasible (i.e. to posses a solution). We then show that solving a special case of PPCR instances directly reduces to find a shortest common supersequence in a particular sequence set. We propose an integer formulation based on this reduction to solve general case instances. Using this formulation we present some experimental results where large instances coming from the nuclear fuel renewal problem are solved to optimality. In order to produce a solution for non-feasible PPCR instances, we introduce some locations for PPCR instances where a piece can be temporarily hold if required. We show that these locations correspond to Steiner nodes in the graph model and we then extend the integer formulation for the resulting Steiner PPCR