What people are saying - Write a review
We haven't found any reviews in the usual places.
Second Order Singular Extremals
The Ubiquity of Fullers Phenomenon
5 other sections not shown
Other editions - View all
absolute value admissible trajectory Assume b.c.r. solutions boundary conditions chattering arcs chattering trajectories codimension constant coordinates Corollary corresponding Denote diffeomorphism differential eigenvalues equals equation exists fixed point Fuller's problem function grad Hamiltonian system Hamiltonian vector field Hence higher order homeomorphic implicit function theorem implies inequality infinite number initial point instant intersect invariant manifold Kupka's Lagrangian manifold Let us consider Let us demonstrate Lowden's problem matrix maximum condition nonzero number of switches obtain one-dimensional optimal control optimal solution optimal synthesis optimal trajectories parabola parameter piecewise smooth Poincare mapping Poisson brackets polynomial Pontryagin's maximum principle Problem 5.2 Proof Proposition prove singular arc singular extremals singular manifold singular solutions singular trajectories smooth manifold solution of system solution to Problem space submanifold sufficiently small switching curve switching surface tangent target manifold Theorem 3.1 trajectories of system transversality two-dimensional variables vector velocity zero