论文标题
最佳控制问题的非主题延续方法具有均衡约束
A Non-Interior-Point Continuation Method for the Optimal Control Problem with Equilibrium Constraints
论文作者
论文摘要
在这项研究中，我们关注具有平衡约束（OCPEC）的最佳控制问题的数值解决方案方法。由于缺乏约束规律性和严格可行的内部点，解决OCPEC非常具有挑战性。为了有效地解决OCPEC，我们首先放宽了离散的OCPEC以恢复约束规律性，然后将其karush-kuhn--tucker（KKT）条件映射到一个扰动的方程系统中。随后，我们提出了一种新型的两阶段解决方案方法，称为非接口延续方法，以解决扰动系统。在第一阶段，采用了一种使用牛顿方法来解决扰动系统的非关键点方法，并使用专用的优点函数全球化收敛。在第二阶段，使用一种预测器 - 校正延续方法来跟踪解决方案轨迹作为扰动参数的函数，从第一阶段获得的解决方案开始。所提出的方法将KKT矩阵定期，并且不会强制迭代保留在可行的内部中，从而减轻了求解OCPEC的数值困难。在某些假设下分析了收敛属性。数值实验表明，与内点方法相比，所提出的方法可以准确跟踪解决方案轨迹，同时要求较小的计算时间。
In this study, we focus on the numerical solution method for the optimal control problem with equilibrium constraints (OCPEC).It is extremely challenging to solve OCPEC owing to the absence of constraint regularity and strictly feasible interior points. To solve OCPEC efficiently, we first relax the discretized OCPEC to recover the constraint regularity and then map its Karush--Kuhn--Tucker (KKT) conditions into a perturbed system of equations. Subsequently, we propose a novel two-stage solution method, called the non-interior-point continuation method, to solve the perturbed system. In the first stage, a non-interior-point method, which solves the perturbed system using the Newton method and globalizes convergence using a dedicated merit function, is employed. In the second stage, a predictor-corrector continuation method is utilized to track the solution trajectory as a function of the perturbed parameter, starting at the solution obtained in the first stage. The proposed method regularizes the KKT matrix and does not enforce iterates to remain in the feasible interior, which mitigates the numerical difficulties of solving OCPEC. Convergence properties are analyzed under certain assumptions. Numerical experiments demonstrate that the proposed method can accurately track the solution trajectory while demanding significantly less computation time compared to the interior-point method.
