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SUMMARY:Embedded Optimization for Optimal Control of Mechatronic Systems -
  Professor Moritz Diehl (K.U. Leuven)
DTSTART:20100507T130000Z
DTEND:20100507T140000Z
UID:TALK21505@talks.cam.ac.uk
CONTACT:Dr Ioannis Lestas
DESCRIPTION:Many branches of engineering employ linear mappings between so
 me input and\noutput sequences\, most prominently in control engineering a
 nd in signal\nprocessing. Examples are PID or other linear controllers\, t
 he Kalman\nFilter\, as well as the many filters used in  sound processing 
 e.g.\nin loudspeakers or hearing aids. These linear maps are usually only 
 useful\nfor one special set of conditions\, when no constraints are violat
 ed\, while\nthey need to be adapted whenever the conditions change.\n\nA c
 ompletely different approach is the following: we generate a map\nbetween 
 inputs and outputs\nvia embedded optimization\, i.e. the outputs are gener
 ated as the solution\nof parametric optimization problems that are solved 
 again and again\, each time\nfor different\nvalues of the input\nparameter
 s. This approach directly generates a nonlinear map between\ninputs and ou
 tputs\, and allows to easily incorporate constraints and user\ndefined obj
 ectives. It can be shown that this\napproach is able to generate any conti
 nuous input-output map even if we\nrequire the optimization problems to be
  convex in both inputs and\noutputs\, which is the most favourable case [1
 ].\n\nThe structure of the embedded optimization problems needs to be expl
 oited\nto the maximum\, as many applications require sampling times in the
  order\nof milli or even microseconds. We present four structure exploitin
 g\nalgorithms that were used in applications:\n\n(a) a convex time transfo
 rmation for time optimal robot arm control [4]\n\n(b) online active set st
 rategy for an optimal pre-filter for machine tools\n[3]\n\n(c) nonlinear r
 eal-time iterations for model predictive control of power\ngenerating kite
  systems [2]\n\n(d) a duality and Fourier based approach to optimal clippi
 ng in hearing\naids.\n\nThe talk will present joint work with J. Swevers\,
  M. Moonen\, J. De\nSchutter\, T. Van Waterschoot\,\nL. Vanden Broeck\, D.
  Verscheure\, B. Houska\, H.J. Ferreau\, and B. Defraene.\n\nReferences\n\
 n[1] M. Baes\, M. Diehl\, and I. Necoara. Every continuous nonlinear contr
 ol\nsystem can be\nobtained by parametric convex programming. IEEE Transac
 tions on Automatic\nControl\,\n53(8):19631967\, September 2008.\n\n[2] A. 
 Ilzhoefer\, B. Houska\, and M. Diehl. Nonlinear MPC of kites under\nvaryin
 g wind conditions\nfor a new class of large scale wind power generators. I
 nternational\nJournal of Robust and\nNonlinear Control\, 17(17):15901599\,
  2007.\n\n[3] L. Van den Broeck\, M. Diehl\, and J. Swevers. Embedded opti
 mization for\ninput shaping.\nIEEE Transactions on Control System Technolo
 gy\, 2009. In press.\n\n[4] D. Verscheure\, B. Demeulenaere\, J. Swevers\,
  J. De Schutter\, and M. Diehl. Time-optimal\npath tracking for robots: a 
 convex optimization approach. IEEE\nTransactions on Automatic Control\, 20
 09. Accepted for publication.\n
LOCATION: Cambridge University Engineering Department\, LR5
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