New Second-Order Optimality Conditions for Variational Problems with C 2 -Hamiltonians
Vera M. Zeidan · SIAM Journal on Control and Optimization · 2001
The generalized problem of Bolzawith a C 2 -Hamiltonian is considered. Necessary and sufficient conditions are obtained, respectively, in terms of the accessory problem, the existence of conjoined basis, and the existence of a solution to a Riccati equation with boundary conditions. No strengthened Legendre--Clebsch condition is required. When applied to a general optimal control problem, these results include and generalize known results.