Second order optimality conditions in the smooth case and applications in optimal control

By Bernard Bonnard, Jean-Baptiste Caillau, Emmanuel Trélat. 2007

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Shape deformation analysis from the optimal control viewpoint (2014, background): “As is well-known in optimal control theory, this coercivity assumption of the bilinear form (∂(2) uJA)(u∗,λ∗,μ) is actually equivalent to the nonexistence of conjugate points of the optimal curve q∗ on [0, 1] (see [9, 10] for this theory and algorithms of computation).”
Optimal location of controllers for the one-dimensional wave equation (2013, unknown): “We used the code COTCOT (see [2]).”
The turnpike property in finite-dimensional nonlinear optimal control (2014, unknown): “The conjugate point theory allows one to test the local optimality status of an extremal, solution of the equations of the Pontryagin maximum principle (see [10] for a survey on this theory and algorithms).”