基于精细积分的瞬时最优控制算法

Instantaneous optimal control algorithm based on precise integration

对于实时控制中测量得到的等间距离散信号,可合理地认为其在每个时间间隔内线性变化。通过在瞬时最优控制算法中用精确积分代替以往采用的近似积分公式,从而给出了精细瞬时最优控制算法,包括精细瞬时闭环最优控制,精细瞬时开环最优控制和精细瞬时开闭环最优控制。这些算法具有精细积分高精度的特点,对于时间步长较大的情况仍可给出比拟于精确解的数值结果。三种算法虽然形式不同,但在理想控制环境下其控制效果完全相同。数值算例表明了本文算法高精度及有效性。

It is reasonable to consider the samples measured in real-time control as linear change at evenly spaced intervals in time. By using an exact integration instead of the approximate integration formula in instantaneous optimal control algorithm, the precise instantaneous optimal control algorithms integration are proposed herein, which includes the precise instantaneous optimal open-loop control, precise instantaneous optimal closed-loop control, and precise instantaneous optimal closed-openloop control. These algorithms have high precision advantages of precise integration, and even for quite a long time step they can give the numerical results approaching to the exact solutions. Although the three algorithms proposed in this paper have different expressions, the control efficiencies are the same under ideal control environments. Numerical examples indicate the high precision and effectiveness of the proposed algorithms.