通过无损凸化求解一类数字控制约束最优控制问题的精确解
Exact Solutions to a Class of Constrained Optimal Control Problems via Lossless Convexification for Digital Control
浏览论文内容
中文总结 AI 辅助
针对航空航天应用中线性系统的约束非凸连续时间最优控制问题，利用无损凸化技术转化为凸问题，通过对控制空间有限参数化建立有效数值方法，在航天器着陆问题上验证其有效性，可用于实际航天制导与控制。
中文摘要 AI 辅助
本文建立了一种新的数值可行技术，用于解决航空航天应用中常见的一类线性系统的约束、非凸、连续时间最优控制问题（OCP）。采用无损凸化技术将具有环形控制幅度约束的原始非凸OCP转化为凸问题，然后通过用分段常数函数对控制空间进行有限参数化，建立了一种有效的数值方法，该方法能保证精确解，同时确保在紧凑时间间隔内满足不可数的约束族。该方法在一个涉及三个自由度的航天器着陆问题上得到了验证，突出了其在实际航天制导和控制任务中的潜力。
英文摘要
This article establishes a new numerically viable technique for solving a class of constrained, nonconvex, continuous-time optimal control problems (OCPs) for linear systems that commonly arise in aerial and aerospace applications. The lossless convexification technique is employed to translate the original nonconvex OCP with annular control magnitude constraints into a convex problem, and then by finitely parametrizing the control space with piecewise constant functions, an efficient numerical approach is established that guarantees exact solutions while ensuring the satisfaction of an uncountable family of constraints over a compact time interval. The effectiveness of the approach is demonstrated on a spacecraft landing problem involving three degrees of freedom (DoF), underscoring its potential for real-world aerospace guidance and control tasks.
