The structure of time-optimal trajectories for single-input systems in the plane: the general real analytic case
The structure of time-optimal trajectories for single-input systems in the plane: the general real analytic case
复制标题
平面上单输入系统的时间最优轨迹结构：一般实解析案例
DOI：
10.1137/0325048
复制
发表时间：
1987
影响因子：
2.2
通讯作者：
H. Sussmann
中科院分区：
文献类型：
--
作者：
H. Sussmann
对于控制线性进入平面上的任意单输入实解析系统，我们证明了时间最优轨迹是“砰-砰”和奇异圆弧的有限级联，具有局部切换次数的界。除了真实的解析性之外，不做任何“非简并”的假设。分析通过应用我们之前在非退化$C^\inty$系统上的结果来研究每个点的邻域上的轨迹的行为，除了一组离散的“分支点”中的点。然后结合控制论的论点和次解析集合论的使用来处理分支点。
For arbitrary single-input real analytic systems in the plane, in which the control enters linearly, we prove that the time-optimal trajectories are finite concatenations of “bang-bang” and singular arcs, with local bounds on the number of switchings. No “nondegeneracy” assumption is made other than real-analyticity. The analysis proceeds by applying our previous results on nondegenerate $C^\infty $ systems to study the behavior of the trajectories on a neighborhood of every point, except for the points in a discrete set of “branch points.” The branch points are then handled by a combination of control-theoretic arguments and the use of subanalytic set theory.