Fixed Final Time: Tests for a Minimum
Before going on to the second differential, two tests for a minimal control are derived. The Weierstrass condition is based on strong variations, which means that control changes are large but that state changes are small. The Weierstrass condition requires that the Hamiltonian be an absolute minimum with respect to the control at every point of a minimal path. The Legendre-Clebsch condition is obtained by reducing strong variations to weak variations. It requires that the Hamiltonian be a local minimum with respect to the control at every point of the minimal path.
KeywordsOptimal Path Strong Variation Minimal Path Weak Variation Navigation Problem
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