论文标题
变体的计算和广义功能的最佳控制
Calculus of variations and optimal control for generalized functions
论文作者
论文摘要
我们提出了一定的变化和最佳控制的高阶计算结果的某些结果。该框架是普通平滑功能的类别，其中包括Schwartz分布，同时共享许多具有普通平滑功能的非线性属性。我们证明了高阶欧拉 - 拉格朗日方程，以差异形式的d'Alembert原理，杜波伊斯 - 雷蒙德最佳条件和诺伊特定理。我们启动了最佳控制理论，证明了最大原理的薄弱形式和最佳控制的Noether定理。我们对奇异长度摆的研究结束，两种介质和具有单数频率的Pais-uhlenbeck振荡器抑制了振荡。
We present an extension of some results of higher order calculus of variations and optimal control to generalized functions. The framework is the category of generalized smooth functions, which includes Schwartz distributions, while sharing many nonlinear properties with ordinary smooth functions. We prove the higher order Euler-Lagrange equations, the D'Alembert principle in differential form, the du Bois-Reymond optimality condition and the Noether's theorem. We start the theory of optimal control proving a weak form of the Pontryagin maximum principle and the Noether's theorem for optimal control. We close with a study of a singularly variable length pendulum, oscillations damped by two media and the Pais-Uhlenbeck oscillator with singular frequencies.
