Exponential sensitivity and turnpike analysis for linear quadratic optimal control of general evolution equations
Exponential sensitivity and turnpike analysis for linear quadratic optimal control of general evolution equations
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DOI：
10.1016/j.jde.2019.11.064
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发表时间：
2020-06
影响因子：
2.4
通讯作者：
L. Grüne;M. Schaller;A. Schiela
中科院分区：
文献类型：
--
作者：
L. Grüne;M. Schaller;A. Schiela
本文分析了一般发展方程所支配的线性二次型最优控制问题的灵敏度，其中控制算子是有界的或容许的。我们表明，如果问题是稳定的和可检测的，极值方程的解决方案可以有界的右手边，包括初始数据的界限是独立的时间范围。因此，极值方程扰动的影响随时间呈指数衰减。该属性可以例如用于为模型预测控制方案构造有效的空间和时间离散化。进一步，我们得到了一般半群的无界容许控制的一个收费公路性质。
We analyze the sensitivity of linear quadratic optimal control problems governed by general evolution equations with bounded or admissible control operator. We show, that if the problem is stabilizable and detectable, the solution of the extremal equation can be bounded by the right-hand side including initial data with the bound being independent of the time horizon. Consequently, the influence of perturbations of the extremal equations decays exponentially in time. This property can for example be used to construct efficient space and time discretizations for a Model Predictive Control scheme. Furthermore, a turnpike property for unbounded but admissible control of general semigroups can be deduced.