线性脉冲控制系统的能控性与最优控制

首先讨论了一类线性随机脉冲控制系统的精确能控性质,给出了该类控制系统的脉冲精确能控的等价的代数判据.然后提出了一个确定性的二维线性脉冲控制系统的时间-脉冲强度最优控制问题;利用动态规划原理,给出了脉冲最优控制的反馈形式和值函数的显式表达式;说明了值函数在整个平面上是连续的,在左右两个半平面的内部还是连续可微的.

Controllability and Optimal Control of Linear Impulsive ControlSystems

The impulsive exact controllability is first discussed for a class of linear stochastic impulsive control systems, and an equivalent algebraic criterion is given for their impulsive exact controllability. Then, the optimal control problem is formulated for a deterministic two-dimensional linear impulsive control system under the cost functional of time and impulse amplitude. Via a dynamic programming, the optimal impulsive control is given in its feedback form, and the value function is given in its explicit form. The value function turns out to be continuous in the whole plane, and is even continuously differentiable in the interiors of both right and left half planes.