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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