Yes if the context, the list of variables defining the motion control problem, is dimensionally similar. Here we show that by modifying the problem formulation using dimensionless variables, we can re-use the optimal control law generated numerically for a specific system to a sub-space of dimensionally similar systems. This is demonstrated, with numerically generated optimal controllers, for the classic motion control problem of swinging-up a torque-limited inverted pendulum. We also discuss the concept of regime, a region in the space of context variables, that can help relax the condition on dimensional similarity. Futhermore, we discuss how applying dimensionnal scaling of the input and output of a context-specific policy is equivalent to substituing the new systems parameters in an analytical equation for dimentionnaly similar systems. It remains to be seen if this approach can also help generalizing policies for more complex high-dimensional problems.

翻译：是的，如果上下文（即定义运动控制问题的变量列表）在量纲上相似。我们在此证明，通过使用无量纲变量修改问题表述，可以将针对特定系统数值生成的最优控制律复用于量纲相似系统的子空间。这一结论通过数值生成的最优控制器在经典运动控制问题——扭矩受限倒立摆的摆起控制中得到验证。我们还讨论了"机制"（regime）的概念，即上下文变量空间中的一个区域，它有助于放宽量纲相似条件。此外，我们讨论了如何对特定上下文的策略进行输入输出的量纲缩放，这等价于将新系统参数代入量纲相似系统的解析方程中。该方法是否也能帮助推广更复杂高维问题的策略，仍有待进一步研究。