Periodic optimal control problems (POCPs) based on dynamic models holding invariants are often problematic to treat using standard numerical methods. The difficulty stems from a failure of standard constraint qualifications and typically hinders the convergence of the numerical solver, or even defeats it. Optimization problems having weak constraint qualifications can be treated using dedicated solvers, at the price of a more involved algorithmic. In this paper, we analyze the constraint qualification of POCPs holding invariants, and propose three simple and computationally inexpensive modifications of the formulation that allow for a recovery of linear independence constraint qualification, while not affecting the second-order sufficient conditions for optimality. Hence, the resulting POCP can be tackled via standard solvers, without special treatment. The application of these approaches is detailed for the case of POCPs holding index-reduced differential-algebraic equations and representations of the SO (3) Lie group.

中文翻译：

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存在不变量时具有周期性约束的数值最优控制


使用标准数值方法处理基于保持不变量的动态模型的周期性最优控制问题 (POCP) 通常会出现问题。该困难源于标准约束条件的失败，并且通常会阻碍数值求解器的收敛，甚至使其失效。具有弱约束资格的优化问题可以使用专用求解器来处理，但代价是更复杂的算法。在本文中，我们分析了保持不变量的 POCP 的约束条件，并提出了三种简单且计算成本低廉的公式修改，允许恢复线性独立约束条件，同时不影响最优性的二阶充分条件。因此，生成的 POCP 可以通过标准求解器来解决，无需特殊处理。这些方法的应用针对 POCP 持有指数约简微分代数方程和 SO (3) 李群表示的情况进行了详细介绍。