Determining the Sufficiency in Optimal Control without the Strengthened Condition of Legendre
Recent Advances in Mathematical Research and Computer Science Vol. 4,
12 November 2021
,
Page 99-112
https://doi.org/10.9734/bpi/ramrcs/v4/2119E
Abstract
In this study, we construct a sufficiency theorem for an unconstrained Lagrange fixed-endpoint problem that offers sufficient conditions for processes that do not satisfy the traditional nonsingularity assumption, i.e., the new sufficiency theorem does not impose the strengthened Legendre condition. In contrast to various generalisations of conjugate points, solutions of certain matrix Riccati equations, invariant integrals, or the Hamiltonian-Jacobi theory, the latter leverages explicitly the positivity of the second variation in the demonstration of sufficiency.
- Optimal control
- sufficient conditions for optimality
- strong minima
- singular extremals
- strengthened legendre-clebsch condition