论文标题
直接搭配的二阶数值最佳控制
Direct Collocation for Numerical Optimal Control of Second-Order ODE
论文作者
论文摘要
机械系统通常由二阶普通微分方程（ode）建模，该方程式（ode）以$ \ ddot {q} = f（t，q，\ dot {q}）$采用表单。虽然已经研究了针对这些方程式量身定制的仿真方法，但在直接最佳控制方法中使用它们很少。实际上，标准方法是执行国家扩展，并将速度增加到州。这种方法的主要缺点是决策变量的数量增加了一倍，这可能会损害由此产生的优化问题的性能。在本文中，我们提出了一种针对二阶颂歌量身定制的方法。在理论方面和数值示例中，我们都将其与标准方面进行了比较。值得注意的是，我们表明，量身定制的配方可能会改善直接搭档方法的性能，以解决更限制的形式的二阶ode $ \ ddot {q} = f（t，q）$的最佳控制问题。
Mechanical systems are usually modeled by second-order Ordinary Differential Equations (ODE) which take the form $\ddot{q} = f(t, q, \dot{q})$. While simulation methods tailored to these equations have been studied, using them in direct optimal control methods is rare. Indeed, the standard approach is to perform a state augmentation, adding the velocities to the state. The main drawback of this approach is that the number of decision variables is doubled, which could harm the performance of the resulting optimization problem. In this paper, we present an approach tailored to second-order ODE. We compare it with the standard one, both on theoretical aspects and in a numerical example. Notably, we show that the tailored formulation is likely to improve the performance of a direct collocation method, for solving optimal control problems with second-order ODE of the more restrictive form $\ddot{q} = f(t, q)$.
