发展包含的可控性

Controllability of evolution inclusion

可控性理论是微分包含的基本内容之一.利用凝聚映射的不动点定理给出了一类发展包含的可控性的充分条件,处理问题的方法是基于解的积分表示,将所讨论的问题转化为集值积分算子的不动点问题.在多值函数F(t,x)取有界闭凸值,关于时间变量t可测,关于状态变量x上半连续时,证明了系统的可控性.

Controllability is a basic content of differential inclusions. By applying a fixed pointed theorem for condesing maps, the sufficient conditions of controllability are given. This method is based on integral expression of solutions, the problem can be converted into fixed point problem of single -valued integral operators. When F（t,x） takes bounded, closed, convex valued, and is measurable about time variable t, is upper semi - continuous about state variable x, the authors prove the controllability of the system.