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Synthesis of the Time-Optimal Motion of an Oscillator along a Broken-Line Path

机译:振荡器沿虚线路径的时间最优运动的合成

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摘要

A planar problem of the time-optimal displacement of a two-dimensional oscillator into a given point on a broken-line path with the suppression of relative oscillations in the end of the control process is studied. It is assumed that the speed of the equilibrium position is controllable within prescribed bounds and the initial position is arbitrary. The examined system of equations turns out to be nonsmooth. Within the asymptotic approach (the control actions are relatively small), a program and synthesis of optimal controls, as well as optimal trajectories and the minimal time of motion for arbitrary initial data, are constructed. The structure of synthesis is analyzed, and some qualitative effects are discovered. In particular. The optimal time of motion is found to be a discontinuous function of the state variables. The results can be of interest in solving the problems of precision control of complex technical systems containing internal moving elements.
机译:研究了在控制过程结束时二维振荡器在虚线路径上的时间最佳位移到给定点并抑制相对振荡的平面问题。假设平衡位置的速度在规定的范围内是可控制的,并且初始位置是任意的。检验的方程组证明是不光滑的。在渐近方法(控制动作相对较小)中,构建了最优控制的程序和综合,以及任意初始数据的最优轨迹和最小运动时间。分析了合成的结构,发现了一些定性作用。特别是。发现最佳运动时间是状态变量的不连续函数。该结果对于解决包含内部运动元件的复杂技术系统的精确控制问题可能是有意义的。

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