## On the Optimality of a Totally Singular Vector Control: An Extension of the Green's Theorem Approach to Higher Dimensions, Volume 305 |

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AJ<fs(t approach to higher arc is optimum assumed comparison trajectories contained complete system Control Appearing Linearly control are singular control problem control set determine differential equations 1.5 dimensional nonlinear systems dynamical system l.l equation l.l equations 5«3 equivalent pfaffian Euler-Lagrange equations evaluate the optimality family of surfaces given point Green's theorem approach Green's theorem technique Hamiltonian higher dimensions hyper hypersurface W(t,x hypersurfaces are given hypersurfaces are obtained independent interpreted as singular J.S.I.A.M. Control Jordan curve line integral n-dimensional Green's theorem need only n-1 neighborhood of accessibility number of hypersurfaces Optimal Control optimal totally singular order n-l parameter partial differential equations pfaffian system pfaffian x)dx problem l.l satisfying the pfaffian simple simply connected single pfaffian singular hypersurfaces singular problem singular vector control system of order system of partial tangent vectors totally singular arc totally singular control totally singular vector trajectories satisfying transfer transversality condition unique pfaffian vector controls governing yields