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.
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Rockafellar, R.T. Hamilton–Jacobi Theory and Parametric Analysis in Fully Convex Problems of Optimal Control. Journal of Global Optimization 28, 419–431 (2004). https://doi.org/10.1023/B:JOGO.0000026459.51919.0e
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DOI: https://doi.org/10.1023/B:JOGO.0000026459.51919.0e