For a system dx/dt=f(x,u), x(0)=x/sup 0/, with x in IR/sup 2/, u in U contained in IR/sup 2/, and f sufficiently smooth and 'generic', it is shown that the number of 'corners' (or vertices) of the time T reachable set Omega /sub T/ does not exceed the number of vertices of U. Moreover, for any trajectory x(t), leading to a vertex x=x(T) of Omega /sub T/, the control u(t) satisfies u(t) identical to u, t in (0,T), with u a vertex of U. A particular case of f(x,u)=Ax+(Bx)u is considered, where the above genericity conditions take especially simple form.
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机译：对于系统Dx / dt = f（x，u），x（0）= x / sup 0 /，用IR / SUP 2 /，U中包含的U IR / SUP 2 /，F足够平滑和“通用”，结果表明，时间t可达设定的“角落”（或顶点）的数量ω/ sub t /不超过U的顶点数量，对于任何轨迹x（t），引领对于OMEGA / SUB T /的顶点x = x（t），控制U（t）满足与U的UA（0，T）相同的U（T），UA顶点UA顶点f的F （X，U）= AX +（BX）U被认为是上述常见条件采用特别简单的形式。
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