论文标题
具有有限控制资源的非线性控制系统的一组轨迹和整体漏斗的近似
Approximations of the Set of Trajectories and Integral Funnel of the Nonlinear Control Systems with Limited Control Resources
论文作者
论文摘要
在本文中，考虑了由非线性普通微分方程描述的一组轨迹和控制系统的积分漏斗的近似值，并考虑了对控制函数的积分约束。一组可接受的控制功能由一个集合取代，该集合由有限数量的分段组合控制功能组成。结果表明，由有限数量的分段组分控制功能生成的轨迹集是一组轨迹的内部近似值。此外，通过适当的欧拉（Euler）的断线代替了分段恒定控制功能生成的每个轨迹，并证明由有限数量的欧拉（Euler）破碎线组成的集合是给定控制系统的轨迹集的近似值。通过由一个有限数量的点组成的集合，将系统积分漏斗的近似值近似。
In this paper approximations of the set of trajectories and integral funnel of the control system described by nonlinear ordinary differential equation with integral constraint on the control functions are considered. The set of admissible control functions is replaced by a set, consisting of a finite number of piecewise-constant control functions. It is shown that the set of trajectories generated by a finite number of piecewise-constant control functions is an internal approximation of the set of trajectories. Further, each trajectory generated by a piecewise-constant control function is substituted by appropriate Euler's broken line and it is proved that the set consisting of a finite number of Euler's broken lines is an approximation of the set of trajectories of given control system. An approximation of the system's integral funnel by a set consisting of a finite number of points is obtained.
