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
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