CAP Research Roulette
Seminars run by PhD students and postdocs with the Control and Power Group
Every week, an invited speaker gives a talk on a relevant topic (preferably in control and power) consisting of a 20-minute presentation followed by a 10-minute discussion. The content of talks can be
- conference contributions,
- initial research proposals,
- preparation for Early Stage Assessment/Late Stage Review, or
- tutorials on topics of the speaker's expertise.
After the talk, the participants can enjoy coffee and snacks (funded by the group) together in the Faraday Cage on EEE Level 6 and continue the discussion.
The CAP Research Roulette is open to everyone in the Control and Power Group. MSc students from Control Systems and Future Power Network Courses, who are willing to continue pursuing an academic career, are also strongly encouraged to participate.
Talk of the week
Title: Integral Penalty Methods for Numerical Optimal Control and Modified Augmented Lagrangian Methods for Their Efficient Solution
Speaker: Martin Neuenhofen
Venue: EEE 1109B
Date and Time: Wednesday, 08/01/2020, 15:00-15:30
Abstract: This talk with mathematical focus presents two numerical methods in the context of solving optimal control problems.
The integral penalty discretization is a direct transcription scheme for optimal control problems in alternative to, e.g., direct collocation methods. In contrast to the latter, the residuals of equality path constraints are not forced to zero only at collocation points but instead globally via a quadratic integral penalty term. Dr Kerrigan and I were able to prove convergence under milder assumptions than for typical direct collocation methods such as trapezoidal, Hermite-Simpson, and certain orthogonal direct collocation methods. Numerical experiments suggest that the method is attractive in particular for solving high-index DAE and general singular-arc optimal control problems, where direct collocation methods can sometimes struggle.
From the penalty discretization results a finite dimensional optimization problem with an inconsistent large quadratic penalty term. Instead of solving it with a quadratic penalty method --that is, solution with successively increasing penalty parameter-- we devise a modified augmented Lagrangian method that allows us to minimize a quadratic penalty function. The modification is necessary because the original augmented Lagrangian method is only designed for (consistent) equality constrained optimization problems. The modification is crucial because otherwise the quadratic penalty function would be numerically challenging to solve.
Biography: Martin Peter Neuenhofen completed his MSc (Computational Engineering) from RWTH Aachen during his full-time employment at the Mercedes AMG Petronas Formula 1 Team, where he worked on their optimal control solver. He received the International Doctoral Fellowship scholarship at the University of British Columbia. He is currently a PhD student at Imperial College London. His research interests are numerical analysis for direct transcription schemes, nonlinear programming, and distributed computing.
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