Fast Algorithm for Fuel-Optimal Impulsive Control of Linear Systems With Time-Varying Cost

• 成果类型: Article
• 署名作者: Koenig, Adam W.; D'Amico, Simone
• 署名单位: Stanford University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3027804
• 发表日期: 2021
• 页码: 4029-4042
• 关键词: Space vehicles; cost function; optimal control; Heuristic algorithms; Robustness; computational modeling; computational methods; Linear systems; optimization algorithms; Time-varying systems

摘要

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.