We propose a novel direct transcription and solution method for solving nonlinear, continuous-time dynamic optimization problems. Instead of forcing the dynamic constraints to be satisfied only at a selected number of points as in direct collocation, the new approach alternates between minimizing and constraining the squared norm of the dynamic constraint residuals integrated along the whole solution trajectories. As a result, the method can 1) obtain solutions of higher accuracy for the same mesh compared to direct collocation methods, 2) enables a flexible trade-off between solution accuracy and optimality, 3) provides reliable solutions for challenging problems, including those with singular arcs and high-index differential algebraic equations.

中文翻译：

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以指定精度求解动态优化问题：使用集成残差的替代方法

我们提出了一种新的直接转录和求解方法，用于解决非线性、连续时间动态优化问题。与在直接搭配中仅在选定数量的点上强制满足动态约束不同，新方法在最小化和约束沿整个解决方案轨迹集成的动态约束残差的平方范数之间交替进行。因此，与直接搭配方法相比，该方法可以 1) 为相同的网格获得更高准确度的解，2) 在解准确度和最优性之间实现灵活的权衡，3) 为具有挑战性的问题提供可靠的解决方案，包括那些具有挑战性的问题奇异弧和高指数微分代数方程。