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SUMMARY:Stochastic Model Predictive Control: Tractability and constraint s
 atisfaction - Professor John Lygeros (Head of the Automatic Control Labora
 tory\, ETH Zurich)
DTSTART:20091201T160000Z
DTEND:20091201T170000Z
UID:TALK21278@talks.cam.ac.uk
CONTACT:Dr Guy-Bart Stan
DESCRIPTION:Exploiting advances in optimization\, especially convex and mu
 lti-parametric optimization\, model predictive control (MPC) for determini
 stic systems has matured into a powerful methodology with a wide range of 
 applications. Recent activity in robust optimization has also enabled the 
 formulation and solution of robust MPC problems for systems subject to var
 ious kinds of worst case uncertainty. For systems subject to stochastic un
 certainty\, however\, the formulation and solution of MPC problems still p
 oses fundamental conceptual challenges. Optimization over open loop contro
 ls\, for example\, tends to lead to excessively conservative solutions\, s
 o optimization over an appropriate class of feedback policies is often nec
 essary. As in the case of robust MPC\, the selection of policies one consi
 ders is crucial and represents a trade-off between the tractability of the
  optimization problem and the optimality of the solution. Moreover\, in th
 e presence of stochastic disturbances hard state and input constraints nee
 d to be re-interpreted as chance constraints\, or integrated chance constr
 aints\, which may be violated with a certain tolerance. This interpretatio
 n\, however\, makes it difficult to enforce hard input constraints dictate
 d by the capabilities of the system and the actuators\, especially if one 
 considers desirable classes of feedback policies such as affine policies. 
 And what guarantees can one provide in the infinite horizon case\, given t
 hat the system evolution is obtained by solving an infinite sequence of fi
 nite horizon problems each of which may violate its constraints with a fin
 ite probability? This talk will outline these challenges and propose solut
 ions for some. The resulting stochastic MPC methods will be illustrated on
  benchmark problems and compared with alternatives.
LOCATION:Cambridge University Engineering Department\, Lecture Room 5
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