标题： 非线性优化和最优控制问题中的光滑逻辑约束 显示英文标题

标题： Smooth Logic Constraints in Nonlinear Optimization and Optimal Control Problems

摘要： 在某些最优控制问题中，状态和输入之间的复杂关系无法通过连续约束轻松表示，需要改用离散逻辑。 本文提出了一种方法，可以直接在连续优化框架内纳入此类逻辑约束，从而无需使用二进制变量或专用求解器。 我们的方法以最小假设将任意逻辑约束重新表述为最大-最小约束，并通过在优化问题中引入辅助变量来平滑这些约束。 当这些重新表述的约束被满足时，它们保证原始逻辑条件成立，确保优化过程的正确性。 我们在两个具有复杂逻辑约束的平面四旋翼控制任务中展示了该方法的有效性。 与现有用于在连续优化中编码逻辑的技术相比，我们的方法实现了更快的计算性能和对可行解的改进收敛。 显示英文摘要

摘要： In some optimal control problems, complex relationships between states and inputs cannot be easily represented using continuous constraints, necessitating the use of discrete logic instead. This paper presents a method for incorporating such logic constraints directly within continuous optimization frameworks, eliminating the need for binary variables or specialized solvers. Our approach reformulates arbitrary logic constraints under minimal assumptions as max-min constraints, which are then smoothed by introducing auxiliary variables into the optimization problem. When these reformulated constraints are satisfied, they guarantee that the original logical conditions hold, ensuring correctness in the optimization process. We demonstrate the effectiveness of this method on two planar quadrotor control tasks with complex logic constraints. Compared to existing techniques for encoding logic in continuous optimization, our approach achieves faster computational performance and improved convergence to feasible solutions.