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SUMMARY:Verifying stability of approximate explicit MPC - Professor Morten
  Hovd (Deparment of Engineering Cybernetics\, Norwegian University of Scie
 nce and Technology)
DTSTART:20091127T140000Z
DTEND:20091127T150000Z
UID:TALK20574@talks.cam.ac.uk
CONTACT:Dr Guy-Bart Stan
DESCRIPTION:Explicit MPC can potentially be used for safety critical appli
 cations\, including applications to systems with fast dynamics.  Unfortuna
 tely\, the off-line calculations at the design stage may be excessively de
 manding\, and the required table size to represent the solution may also b
 e unacceptable for some applications.\n\nSeveral authors have therefore pr
 oposed various approximations to the (exact\, optimal) explicit MPC.  In a
 pproximate explicit MPC one generally accepts some degree of sub-optimalit
 y in order to arrive at a simpler solution\, requiring fewer regions (and 
 therefore also a smaller look-up table).  Key properties of a design proce
 dure for approximate explicit MPC are:\ni) It should not be necessary to f
 ind the exact solution first\, and\nii) It should be possible to ascertain
  the closed loop stability of the approximate solution.\nMost authors guar
 antee stability by starting from an MPC formulation that guarantees stabil
 ity for the exact solution\, and then ensure that the cost of the approxim
 ate solution is 'close' to the cost of the exact solution.  It can then be
  shown that the optimal\ncost function is also a Lyapunov function for the
  approximate solution.\n\nThe talk will focus on alternative approaches to
  guaranteeing stability of approximate explicit MPC.  Two such approaches 
 will be presented:\ni) Refining the approximate solution until it can be s
 hown that the cost function for the approximate solution is a Lyapunov fun
 ction.\nii) Using an LMI formulation to find a piecewise quadratic Lyapuno
 v function for the approximate solution.\nFor the LMI formulation\, a nove
 l relaxation will be proposed.  Numerical examples indicate that this new 
 relaxation is superior to the relaxation in common use for finding PWQ Lya
 punov functions.
LOCATION:Cambridge University Engineering Department\, Lecture Theatre 2
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