The optimal linear-quadratic time-invariant regulator with cheap control
The optimal linear-quadratic time-invariant regulator with cheap control
复制标题
DOI：
10.1109/tac.1979.1102097
复制
发表时间：
1979-08
影响因子：
6.8
通讯作者：
B. Francis
中科院分区：
文献类型：
--
作者：
B. Francis
无限时间线性二次调节器被认为是控制能量的权重趋于零（廉价控制）。首先，研究了极限最优状态和控制轨迹的定性行为。特别是，找到了初始奇点的阶数，并将其与工厂中极点多于零点的数量相关。其次，找出在哪些初始条件下极限最小成本为零（完美调节）。这概括了 Kwakernaak 和 Sivan 的早期结果。最后，通过廉价的控制和准确的观测对稳态 LQG 问题进行了简单的扩展。
The infinite-time linear-quadratic regulator is considered as the weighting on the control energy tends to zero (cheap control). First, a study is made of the qualitative behavior of the limiting optimal state and control trajectories. In particular, the orders of initial singularity are found and related to the excess of poles over zeros in the plant. Secondly, it is found for which initial conditions the limiting minimum cost is zero (perfect regulation). This generalizes an earlier result of Kwakernaak and Sivan. Finally, a simple extension is made to the steady-state LQG problem with cheap control and accurate observations.