CAJ | 학술논문

控制向量参数化方法是求解最优控制问题的一种常用数值方法。它通过离散化控制时域，将控制向量近似地表示成一组参数化的函数。离散化后的时间网格通常是固定的，其划分会影响到最优控制问题数值求解的精度和效率。为了同时优化控制参数和时间网格节点，提出了一种时间节点可变的控制向量参数化方法。推导出了最优控制性能指标对时间参数的导数与对时间分段长度导数之间的关系，得到了性能指标的梯度表达式。用两个经典最优控制实例对所提出的方法进行了测试，结果表明所提出方法能够更好地逼近最优控制轨迹。
공제향량삼수화방법시구해최우공제문제적일충상용수치방법。타통과리산화공제시역，장공제향량근사지표시성일조삼수화적함수。리산화후적시간망격통상시고정적，기화분회영향도최우공제문제수치구해적정도화효솔。위료동시우화공제삼수화시간망격절점，제출료일충시간절점가변적공제향량삼수화방법。추도출료최우공제성능지표대시간삼수적도수여대시간분단장도도수지간적관계，득도료성능지표적제도표체식。용량개경전최우공제실례대소제출적방법진행료측시，결과표명소제출방법능구경호지핍근최우공제궤적。
Control vector parameterization (CVP) is a frequently used numerical method for solving optimal control problems, where the control vector is approximated by a group of parametric functions through time discretization. Usually, the discretized time grid is fixed, and its partition will affect accuracy and performance of the numerical solution of optimal control problem. To optimize both the control parameters and the time grid nodes, a CVP method with variable time nodes was proposed. Based on the derived relationship between the gradients of time nodes and the ones of interval lengths, the gradient equations for parameters were presented. The proposed method was demonstrated to have better approximation ability for the optimal control trajectories on two classic optimal control problems.