Séminaires du Département Génie mathématique et industriel

|Département Génie mathématique et industriel |

Titre : Direct Model Predective Control : A Theoretical and Numerical Analysis

Jeudi 7 juin à 14h – amphi 104 de l’Espace Fauriel.

Présentatrice : Marie‐​Liesse Cauwet.

Résumé : The power sys­tem pro­blem is for­mu­la­ted as a sto­chas­tic deci­sion pro­cess with large constrai­ned action space, high sto­chas­ti­ci­ty and dozens of state variables. Direct Model Predictive Control has pre­vious­ly been pro­po­sed to encom­pass a large class of sto­chas­tic deci­sion making pro­blems. It is a hybrid model which merges the pro­per­ties of two dif­ferent dyna­mic opti­mi­za­tion methods, Model Predictive Control and Stochastic Dual Dynamic Programming. We prove that Direct Model Predictive Control reaches an opti­mal poli­cy for a wider class of deci­sion pro­cesses than those sol­ved by Model Predictive Control (subop­ti­mal by nature), Stochastic Dynamic Programming (which needs a mode­rate size of state space) or Stochastic Dual Dynamic Programming (which requires convexi­ty of Bellman values and a mode­rate com­plexi­ty of the ran­dom value state). The algo­rithm is tes­ted on a multiple‐​battery mana­ge­ment pro­blem and two hydroe­lec­tric pro­blems. Direct Model Predictive Control clear­ly out­per­forms Model Predictive Control on the tes­ted problems.

Titres : Activité en Science des Données à Total

Jeudi 26 avril à 14h – Salle 528 de l’Espace Fauriel à Saint‐Etienne

Présentateur : Michel LUTZ (Total)

Titre : Optimization of computer experiments with multiple responses

Mardi 20 mars, 9h, Espace Fauriel, Amphi 104
Présentateurs : Sonja KUHNT et Dominik KIRCHHOFF (Université de Dortmund)

Résumé : In this talk we present results and on‐​going research from two dif­ferent pro­jects. In engi­nee­ring and natu­ral sciences it has become com­mon prac­tice to replace phy­si­cal expe­ri­ments with com­pu­ter simu­la­tions (black‐​box expe­ri­ments). As these simu­la­tions can be very time‐​consuming and com­plex, often a sur­ro­gate or meta‐​model of the com­pu­ter expe­riment is built first and ana­ly­sis and opti­mi­za­tion are then based on this model. Gaussian pro­cess models, bet­ter known as Kriging models, are wide­ly used for this purpose.

Our first pro­ject is set in the field of tur­bo machines, which play an impor­tant role for the whole pro­cess chain of ener­gy trans­for­ma­tion. A spe­ci­fic impel­ler geo­me­try is simu­la­ted over the entire ope­ra­ting range with regard to its effi­cien­cy. Computer expe­ri­ments fol­lo­wing a space‐​filling desi­gn are run and Gaussian pro­cess models are fit­ted to mul­tiple res­ponses, some of which are to be opti­mi­zed whe­reas others need to be kept within cer­tain bounds. The popu­lar effi­cient glo­bal opti­mi­za­tion (EGO) pro­ce­dure pro­vides a sequen­tial Kriging‐​based opti­mi­za­tion with the expec­ted impro­ve­ment as cri­te­rion. We look at exten­sions of the EGO algo­rithm to mul­tiple res­ponses as well as constraints.

In the second part we deal with com­pu­ter simu­la­tions with mixed conti­nuous and cate­go­ri­cal input variables. The ori­gi­nal Kriging model can only cope with pure­ly conti­nuous inputs. First exten­sions exist to incor­po­rate also cate­go­ri­cal variables. Here, we consi­der three approaches cal­led Exchangeable Correlation, Multiplicative Correlation and Unrestrictive Hypersphere‐​based Correlation that are dif­ferent in terms of their flexi­bi­li­ty and com­pu­ta­tio­nal effort. We intro­duce a new approach, where the num­ber of unk­nown para­me­ters can be cho­sen flexi­bly by the prac­ti­tio­ner. We present first results from a com­pu­ter simu­la­tion of a dis­tri­bu­tion warehouse.