具有振荡、集中和不连续的最优控制问题
Optimal control problems with oscillations, concentrations and discontinuities
摘要：
具有振荡（抖振控制）和集中（脉冲控制）的最优控制问题可以具有积分性能准则，使得控制信号的集中发生在状态信号的不连续处。从泛函分析（各向异性参数化措施）的技术被应用到给出一个精确的意义的积分成本，并允许健全的应用程序的数值方法。我们展示了如何将这可以与拉塞尔层次的半定规划松弛。
英文摘要：
Optimal control problems with oscillations (chattering controls) and concentrations (impulsive controls) can have integral performance criteria such that concentration of the control signal occurs at a discontinuity of the state signal. Techniques from functional analysis (anisotropic parametrized measures) are applied to give a precise meaning of the integral cost and to allow for the sound application of numerical methods. We show how this can be combined with the Lasserre hierarchy of semidefinite programming relaxations.
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