Abstract

Control problems with fully convex Lagrangians and convex initial costs are considered. Generalized conjugacy and envelope representation in terms of a dualizing kernel are employed to recover the initial cost from the value function at some fixed future time, leading to a generalization of the cancellation rule for inf-convolution. Such recovery is possible subject to persistence of trajectories of a generalized Hamiltonian system, associated with the Lagrangian. Global analysis of Hamiltonian trajectories is carried out, leading to conditions on the Hamiltonian, and the corresponding Lagrangian, guaranteeing persistence of the trajectories.

Author information

Contact details are reproduced from the original publication and may be historical.

Rafal Goebel

Center for Control Engineering and Computation, Electrical and Computer Engineering, University of California, Santa Barbara, CA 93106-9650, U.S.A.

rafal@ece.ucsb.edu

Ralph Tyrrell Rockafellar

Dept. of Mathematics, University of Washington, Seattle, WA 98195-4350, U.S.A.

rtr@math.washington.edu

Keywords

  • Convex value functions
  • inf-convolution
  • Hopf-Lax formula
  • nonsmooth Hamiltonian dynamics
  • generalized conjugacy
  • fully convex Lagrangians
  • optimal control

Mathematics Subject Classification

49L20, 93C10; 49N15

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Suggested citation

R. Goebel, R. T. Rockafellar. “Generalized Conjugacy in Hamilton-Jacobi Theory for Fully Convex Lagrangians.” Journal of Convex Analysis 9 (2002), No. 2, 463–473. https://doi.org/10.68381/jca09027

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Published by Heldermann Verlag, 2002. Rights now held by Banach Press.