Hamilton–Jacobi Theory and Parametric Analysis in Fully Convex Problems of Optimal Control

Authors:
R. Tyrrell Rockafellar
Affiliations:
Department of Mathematics, Box 354350, University of Washington, Seattle, WA 98195-4350, USA (e-mail: rtr@math.washington.edu)
Venue:
Journal of Global Optimization
Year:
2004

Citing 2
Cited 1

Convexity in Hamilton--Jacobi Theory I: Dynamics and Duality

SIAM Journal on Control and Optimization
Convexity in Hamilton--Jacobi Theory II: Envelope Representations

SIAM Journal on Control and Optimization

Mordukhovich subgradients of the value function to a parametric discrete optimal control problem

Journal of Global Optimization

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Abstract

For optimal control problems satisfying convexity conditions in the state as well as the velocity, the optimal value is studied as a function of the time horizon and other parameters. Conditions are identified in which this optimal value function is locally Lipschitz continuous and semidifferentiable, or even differentiable. The Hamilton–Jacobi theory for such control problems provides the framework in which the results are obtained.