Controllability and Optimal Control of Linear Impulsive ControlSystems
线性脉冲控制系统的能控性与最优控制

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.