Optimization Online


Necessary Conditions for the Impulsive Optimal Control of Multibody Mechanical Systems

Kerim Yunt(kerimyunt***at***gmx.ch)

Abstract: In this work, necessary conditions for the impulsive optimal control of multibody mechanical systems are stated. The conditions are obtained by the application subdifferential calculus techniques to extended-valued lower semi-continuous generalized Bolza functional that is evaluated on multiple intervals. Contrary to the approach in literature so far, the instant of possibly impulsive transition is considered as a Lebesgue negligible instant. This approach is in comparison to other impulsive necessary conditions consistent with mainstream hybrid system modeling methods in which transitions happen instantaneously. The necessary conditions provide necessary criteria for the determination of optimal transition times and locations. The consideration of certain type of variations at the boundaries give birth to the concepts of internal boundary variations and discontinuous transversality conditions. The concepts are developed by the author and are presented and discussed in [20] and [22] with applications to optimal control. In this work, a characterization of these concepts in terms of upper and lower subderivatives to the extended-valued lower-semicontinuous value functional under several regularity assumptions is given. The properties of the transition sets are discussed.

Keywords: Lagrangian systems, optimal control, impulsive control, nonsmooth analysis, necessary conditions

Category 1: Complementarity and Variational Inequalities

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )


Download: [PDF]

Entry Submitted: 08/31/2008
Entry Accepted: 09/01/2008
Entry Last Modified: 08/31/2008

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Programming Society