The Optimization in Engineering Center OPTEC at K.U. Leuven (Belgium)

invites highly motivated young interdisciplinary researchers with a

solid background in numerical mathematics and computer science to

apply for one of the following PhD or Post-doc positions:

* Optimal Control Methods for Application at a Central Receiver

Thermal Power Plant

(PhD or Post-doc Position)

Aim of the project is to develop and apply optimal control

techniques suitable for the control tasks occuring in the central

receiver thermal power plant built by the solar institute in Juelich.

Besides being a full member of the Optimization in Engineering

Center OPTEC at K.U. Leuven, the Post-doc or PhD student will work in

close collaboration with 4 partner groups in Germany that each have

one three year position dedicated to the joint “virtual Institute on

Central Receiver Power Plants, vICeRP” that was founded on January 29,

2008 (http://idw-online.de/pages/de/news244682).

A first task is to work on system modelling and formulation of

the optimal control problems arising in control of the heliostats, the

airflow in the central receiver, as well as the steam cycle of the

power block of the plant. A second task is to extend existing optimal

control algorithms, or to develop new ones when necessary, to make

them suitable for the application to the solar power plant problems.

A good mathematical background with solid knowledge of numerical

optimal control, and programming skills in C are a prerequisite, as

well as a strong interest in application driven interdisciplinary

work, cooperation skills and knowledge of English. Knowledge of German

and Dutch can be an advantage.

Contact: Prof. Dr. Moritz Diehl (E-mail:

moritz.diehl@esat.kuleuven.be)

* Nonlinear Moving Horizon Estimation for Fault Detection

(PhD or Post-doc Position, 3 years)

Aim of the project is to develop and apply novel techniques for

fault detection that are based on online optimization. Given a system

model as well as the most current sensor data on a window in the past,

the idea is to:

1. To find the most probable explanation for the observed

data by online optimization of the system and disturbance model.

2. To give alarm if this best achievable explanation is still

too improbable.

Besides being a full member of the Optimization in Engineering

Center OPTEC at K.U. Leuven, the Post-doc or PhD student will work in

very close collaboration with the Austrian Center of Competence in

Mechatronics (ACCM) and the Institute for Design and Control of

Mechatronical Systems (Prof. Del Re), both in Linz. Most application

problems will come from within this center and its industrial partners.

A good background in control engineering, mathematics, or

physics and solid knowledge of numerical methods and programming

skills are a prerequisite, as well as a strong interest in application

driven interdisciplinary work, cooperation skills and knowledge of

English. Knowledge of German and Dutch is an advantage.

Contact: Prof. Dr. Moritz Diehl (E-mail:

moritz.diehl@esat.kuleuven.be)

* Convex Dynamic Programming for Applications in Robust Model

Predictive Control and State Estimation

(PhD Position, 4 years)

The project shall explore a large but partly unexplored class of

nonlinear optimal control systems that are connected by the fact that

their dynamic programming (DP) cost-to-go is convex. Of this class the

classical linear quadratic regulator (LQR), a linear control law, and

the linear model predictive controller (MPC), a nonlinear control law,

are the two best-known examples.

Full exploitation of convexity for more general control systems

in this class shall lead to new and computational efficient convex

dynamic programming methods. These can be used for exact and

approximate computation of optimization based feedback controllers

that are applicable in particular to uncertain systems, i.e., robust

model predictive control. Here a dynamic min-max game with nature as

the controllers adverse player needs to be solved, and which is

computationally considerably more demanding than classical MPC.

The project shall investigate the two major questions: (a) What

problem classes are covered by convex dynamic programming? and (b) How

to represent and compute the convex cost-to-go efficiently? Finally,

the concepts shall be transferred to the problem of state estimation,

which in a Bayesian framework deals with probability densities instead

of cost-to-go functions. The negative logarithm of these densities is

in many cases convex, and can thus again be treated by convexity-based

computational methods. The Kalman filter with its multidimensional

Gaussian probability distribution is again only the simplest case of a

considerably larger class of convex filters.

The outcome of the project shall be a sound theoretical

framework for the understanding of control and estimation systems

based on convex dynamic programming, along with new and efficient

open-source algorithms ready for use in practical applications. The

project can build on previous work in the group,

http://www.iwr.uni-heidelberg.de/~Moritz.Diehl/RDP/

A solid background in mathematics and control engineering is a

prerequisite, as well as a strong interest in theoretical convex

optimization, set computations, and algorithm development. Knowledge

of English is required, knowing Dutch is an advantage.

Contacts: Prof. Dr. Moritz Diehl (E-mail:

moritz.diehl@esat.kuleuven.be),

Prof. Dr. Carlos Dorea, OPTEC guest from Feb 2008-Feb 2009

(E-mail:cetdorea@ufba.br)

* Optimization Methods for Distributed Model Predictive Control

(PhD or Post-doc Position)

The position is part of a European project on hierarchical and

distributed model predictive control with partners in Europe and the

US (leaflet). The position at OPTEC has as its aim the development of

decomposition methods, distributed state estimation and MPC. Work will

be both on computational aspects - for example efficient distributed

algorithms and implementations, online initialization for nonlinear

optimization - as well as on convergence questions - for example: when

does a distributed MPC protocol converge to the solution of the

centralized MPC optimization problem?

A good background in control engineering, mathematics, or

physics and solid knowledge of numerical methods in control and

programming skills are a prerequisite, as well as a strong interest in

application driven interdisciplinary work, cooperation skills and

knowledge of English. Knowledge of Dutch is an advantage.

Contacts: Prof. Dr. Moritz Diehl (E-mail:

moritz.diehl@esat.kuleuven.be), Dr. Ion Necoara

* Optimization Based Control Design for Large-Scale Systems

(PhD Position)

The aim of the project is to develop and implement optimization

based methods for solving control design problems for large-scale

systems. In the first stage of the project the emphasis is on

developing polynomial type methods and algorithms and on solving fixed

structure control design problems. As fixed structure design problems

often lead to non convex problems, special attention will be paid to

an appropriate problem formulation and to the use of convex

relaxations (such as convex relaxations of non-convex sets,

sum-of-squares relaxations of positive polynomials). In a next stage

the obtained results will be adapted and extended towards large-scale

systems, with particular attention on developing decentralized control

schemes for interconnected and networked systems. These control

schemes should translate global objectives (on agreement, performance,

robustness, etc.) into local control, adapt easily to changes in the

network and the environment, and scale well with the system or network

size.

Depending of the interest of the candidate his / her individual

PhD project can be steered in the direction of the design of

optimization algorithms, the development of polynomial type methods

for systems and control, or on control strategies for large-scale systems.

A background in numerical mathematics, control engineering and

programming skills are a prerequisite, as well as an interest in

application driven interdisciplinary work, good cooperation skills and

knowledge of English.

Contact: Dr. Wim Michiels (E-mail: wim.michiels@cs.kuleuven.be)

* Optimal Motion Control for Machine Tools

(PhD or Post-doc Position)

The goal of this research project is to develop efficient

methods to optimize point-to-point motion trajectories for machine

tools. Machine tools are mechatronic systems that can often be

described by either a linear time-invariant (LTI) model or a linear

parameter varying (LPV) model. The approach followed in this project

is to combine existing classical cascade or robust linear

time-invariant (LTI) controllers with optimized motion trajectories.

The motion trajectory design will be based on a framework that

was recently developed within OPTEC, and that is a generalization of

the work of Kwakernaak and Smit [1]. The basis is a polynomial spline

of arbitrary order that is optimized with respect to some performance

criteria, and subject to boundary constraints and bounds on the

inputs, outputs, and state variables. A careful selection of

performance criteria and constraints yields a convex program that can

be solved efficiently, allowing us to calculate Pareto-optimal points

for these typically multi-criteria optimization problems.

This framework will be further developed to account for system

uncertainty (robust design) and large system dynamics changes that are

typically described using linear parameter varying (LPV) models.

Possibilities for extensions of the current convexity based

optimization approaches in order to address fully nonlinear models

shall also be investigated.

The emphasis of this project lies on the development of fast and

reliable open-source algorithms to optimize these trajectories, the

analysis of the trade-off between the different design parameters,

e.g. level of continuity of the trajectories, time optimality, level

of residual system vibrations, comparison with other existing motion

trajectory parametrizations, and experimental validation on a linear

motor based pick-and-place machine.

This research will be performed under the joint supervision of

Professor Jan Swevers of the division PMA of the Mechanical

Engineering Department (http://www.mech.kuleuven.be/pma/) and

Professor Moritz Diehl of the division SCD of the Electrical

Engineering Departement (http://www.esat.kuleuven.be/scd/). The work

will profit from concerted programming efforts within the OPTEC team

towards a suite of open-source optimal control software tools.

Candidates for this position (phd or post-doc) shall provide a

detailed CV including names of at least two referees. A thorough

background in control theory, dynamic optimization, and implementation

of numerical algorithms is required. Please indicate your background

with respect to these items clearly in your CV. Experience in the

practical implementation of controllers is a benefit but not

mandatory. However, interest for practical control implementation,

programming, and team work is very important.

Contact: Prof. Dr. Moritz Diehl (E-mail:

moritz.diehl@esat.kuleuven.be)

Besides a competitive salary we offer a stimulating research

environment within our young but growing “Center of Excellence on

Optimization in Engineering”, or OPTEC. OPTEC is well connected

internationally with several high ranking international visitors every

month, and encompasses groups from four different departments of K.U.

Leuven [Electrical Engineering (ESAT-SCD), Mechanical Engineering

(MECH-PMA), Chemical Engineering (CHEM-BioTec) and Computer Science

(CS-NATW)]. OPTEC combines altogether 20 professors, 12 postdocs, and

more than 50 PhD students that jointly work on bringing

state-of-the-art optimization methods together with real-world

engineering applications.

Electronic applications (by holders of at least a masters degree)

including a CV, certificates with high school and university marks in

mathematics, physics and computer science, a list of publications,

names of two possible references, and a brief description of your

research interests are most welcome.

Please send them until June 15, 2008 to jobs-at-optec@esat.kuleuven.be.

website link:

http://homes.esat.kuleuven.be/~optec/jobs.php

## Monday, June 2, 2008

### Several PhD positions in Optimization, KU Leuven, Belgium

at
12:12 PM

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