PhD Position: Convex Dynamic Programming for Applications in Robust Model Predictive Control and State Estimation
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)
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.
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)
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.
