Fast Algorithm for Fuel-Optimal Impulsive Control of Linear Systems With Time-Varying Cost
Fast Algorithm for Fuel-Optimal Impulsive Control of Linear Systems With Time-Varying Cost
复制标题
时变成本线性系统燃料最优脉冲控制的快速算法
DOI：
10.1109/tac.2020.3027804
复制
发表时间：
2020
影响因子：
6.8
通讯作者：
S. D’Amico
中科院分区：
文献类型：
--
作者：
Adam W. Koenig;S. D’Amico
本文提出了一种新的快速且鲁棒的算法，该算法提供燃料最佳的脉冲控制输入序列，将线性时变系统在指定时间驱动到所需状态。该算法适用于一类广泛的问题，其中成本表示为控制输入的时变范数函数，从而能够在控制规划问题中包含复杂的操作约束。首先，表明该问题的可达集与使用恒定成本函数的先前工作中的可达集具有相同的属性，从而能够将现有算法与新导出的接触和支持函数结合使用。通过将最优控制问题重新表述为半无限凸程序，还证明了通常研究的引物向量的半无限分量是目标状态下可达集的外向法向量。使用该公式，提出了一种快速且鲁棒的算法，可提供全局最优的脉冲控制输入序列。该算法迭代地将向外法向量的估计细化为目标状态下的可达集合和控制输入时间的最小集合，直到满足用户指定的容差内的最优标准。接下来，通过求解二次规划来计算最优控制输入。该算法通过基于最近提出的小型分布式隐匿/望远镜小卫星任务的具有挑战性的示例问题的模拟进行了验证，这表明所提出的算法的收敛速度比文献中的同类算法快几倍。
This article presents a new fast and robust algorithm that provides fuel-optimal impulsive control input sequences that drive a linear time-variant system to a desired state at a specified time. This algorithm is applicable to a broad class of problems where the cost is expressed as a time-varying norm-like function of the control input, enabling inclusion of complex operational constraints in the control planning problem. First, it is shown that the reachable sets for this problem have identical properties to those in prior works using constant cost functions, enabling use of existing algorithms in conjunction with newly derived contact and support functions. By reformulating the optimal control problem as a semi-infinite convex program, it is also demonstrated that the semi-infinite component of the commonly studied primer vector is an outward normal vector to the reachable set at the target state. Using this formulation, a fast and robust algorithm that provides globally optimal impulsive control input sequences is proposed. The algorithm iteratively refines estimates of an outward normal vector to the reachable set at the target state and a minimal set of control input times until the optimality criteria are satisfied to within a user-specified tolerance. Next, optimal control inputs are computed by solving a quadratic program. The algorithm is validated through simulations of challenging example problems based on the recently proposed miniaturized distributed occulter/telescope small satellite mission, which demonstrate that the proposed algorithm converges several times faster than comparable algorithms in the literature.