Abstract

We study the problem of optimal choice of model parameters with respect to any functional. Locally controllable affine systems and integral functionals depending on the program control are considered. Local controllability of affine systems with nonnegative inputs is proved in the case where the columns multiplying the controls form a positive basis. For such systems, we introduce the local controllability coefficient and pose the problem of its maximization depending on the choice of model parameters. As an example, we consider a very simplified model of an underwater vehicle and study the problem of finding an arrangement of its control propellers in which the energy consumption of the vehicle is minimal.

中文翻译：

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寻找局部可控性最好的模型参数

摘要

我们研究关于任何泛函的模型参数的最优选择问题。考虑了取决于程序控制的局部可控仿射系统和积分泛函。在列与控制相乘形成正基的情况下，证明了具有非负输入的仿射系统的局部可控性。对于此类系统，我们引入局部可控系数，并根据模型参数的选择提出其最大化的问题。作为一个例子，我们考虑一个非常简化的水下航行器模型，并研究寻找其控制螺旋桨的布置的问题，其中航行器的能量消耗最小。