OPTEC today: Benoit Chachuat (global, 11:00), Boris Houska (robust,17:00)
Dear OPTEC Members and Friends,
today we have two events, both on Dynamic Optimization, and both in ESAT Aud. A:
11:00 OPTEC talk on Global Optimization of dynamic systems by Benoit Chachuat (Imperial)
17:00 PhD Defense Boris Houska on Robust Optimization of Dynamic Systems
Benoit Chachuat, Chemical Engineer and optimization expert from Imperial College,
visits us for most of the rest of the week, and is open to meet for short individual discussions.
Please see the abstracts below or on http://www.kuleuven.be/optec/event
Please feel most warmly invited!
Best regards,
Moritz Diehl
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Wed 07 Sep 2011 11:00-12:00, ESAT Aud. A
"Deterministic Global Optimization of Dynamic Systems: State-of-the-Art and Opportunities"
Benoit Chachuat
Centre for Process Systems Engineering, Department of Chemical Engineering, Imperial College London
http://www3.imperial.ac.uk/people/b.chachuat
Abstract
Many chemical processes are inherently dynamic, such as batch, semi-continuous and cyclic processes, while others are operated in an intentionally transient manner through frequent set-point changes. Optimizing such systems gives rise to dynamic optimization problems, which are often nonconvex and exhibit multiple suboptimal solutions. For those applications where a certificate of global optimality is essential, global optimization methods for dynamic systems are clearly warranted. In the first part of the presentation, I will give an overview of the developments in global dynamic optimization over the last 10+ years. The focus will be on deterministic approaches that can guarantee finite convergence to a global solution at an arbitrary precision. The ability to construct tight interval bounds or, better, convex/concave bounds on the dynamic trajectories is pivotal to the efficacy of these approaches. In the second part, I will present a new class of methods developed in my research group for the construction of convex/concave bounds for parametric nonlinear ODEs. These methods build upon verified solution techniques for ODEs and use a combination of Taylor models and McCormick relaxation to propagate the convex/concave bounds. Both theoretical and implementation issues will be discussed and illustrated through several case studies. I will close the presentation with a vision for future developments in global dynamic optimization.
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Wed 07 Sep 2011 17:00-00:00, ESAT Aud. A
"Robust Optimization of Dynamic Systems"
Boris Houska (K.U. Leuven, ESAT-SCD)
Abstract
This thesis is about robust optimization, a class of mathematical optimization problemswhich arise frequently in engineering applications, where unknown process parameters and
unpredictable external influences are present. Especially, if the uncertainty enters via a
nonlinear differential equation, the associated robust counterpart problems are challenging
to solve. The aim of this thesis is to develop computationally tractable formulations
together with efficient numerical algorithms for both: finite dimensional robust optimization
as well as robust optimal control problems.
The first part of the thesis concentrates on robust counterpart formulations which lead to
“min-max” or bilevel optimization problems. Here, the lower level maximization problem
must be solved globally in order to guarantee robustness with respect to constraints.
Concerning the upper level optimization problem, search routines for local minima are
required. We discuss special cases in which this type of bilevel problems can be solved
exactly as well as cases where suitable conservative approximation strategies have to be
applied in order to obtain numerically tractable formulations. One main contribution of this
thesis is the development of a tailored algorithm, the sequential convex bilevel programming
method, which exploits the particular structure of nonlinear min-max optimization problems.
The second part of the thesis concentrates on the robust optimization of nonlinear dynamic
systems. Here, the differential equation can be affected by both: unknown time-constant
parameters as well as time-varying uncertainties. We discuss set-theoretic methods for
uncertain optimal control problems which allow us to formulate robustness guarantees
with respect to state constraints. Algorithmic strategies are developed which solve the
corresponding robust optimal control problems in a conservative approximation. Moreover,
the methods are extended to open-loop controlled periodic systems, where additional
stability aspects have to be taken into account.
The third part is about the open-source optimal control software ACADO which is the basis
for all numerical results in this thesis. After explaining the main algorithmic concepts and
structure of this software, we elaborate on fast model predictive control implementations
for small scale dynamic system as well as on an inexact sequential quadratic programming
method for the optimization of large scale differential algebraic equations. Finally, the
performance of the algorithms in ACADO is tested with robust optimization and robust
optimal control problems which arise from various fields of engineering.
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