Solving Robust Optimal Control Problems, with Application to Spacecraft Entry, Descent and Landing

随着航天机构和企业计划未来的火星任务，连续的航天器着陆和大的有效载荷要求，新的进入车辆目前正在概念化。这些航天器需要能够实现前所未有的着陆精度的控制算法，最佳地管理热负荷和推进剂的使用，同时在高度不确定的大气环境中运行。考虑到这一应用，该研究项目旨在通过忠实地包括模型的不确定性和非线性来解决鲁棒最优控制问题（OCP），实现比使用线性时变基函数的反馈策略的当前算法更高的性能。研究将集中于使用更一般的神经网络作为基函数。首先，为了解决最优控制问题--这可以被视为求解微分代数方程（DAE）系统--最初的重点将是加权残差方法，继续研究小组以前的工作。将进行研究，在成熟的算法，有效地用于解决DAE所产生的最优控制问题。尽管方法是通用的-能够解决各种各样的OCP（及DAE）-特别关注航天器进入问题，针对问题的不确定性和非线性性质进行研究。其次，针对研究问题的大气环境、敏感初始条件和飞行器设计参数的固有不确定性，将研究如何模拟这些不确定性。最初专注于多项式混沌展开和基于样本的不确定性作为工具来显式地表示，传播和操作变量的不确定性，这已被证明比传统的Monte Carlo方法具有更好的性能。第三，考虑到航天器再入问题的非线性和非光滑特性（如三维姿态动力学、超声速和高超声速效应、火箭分级和可展开结构等），本文提出了一种新的控制算法。将评估非线性和非平滑基函数的使用。以神经网络为重点，研究如何在鲁棒最优控制问题中最好地使用它们。重点将放在包括车辆参数（例如，隔热板厚度、质心位置、致动器限制等）。在动态优化过程中，为某一特定使命规范提供最佳航天器设计。2该研究项目旨在对现有方法、理论和技术进行重大突破和改进。此外，还将开发用于解决微分方程、最优控制问题、轨道优化问题和整个航天器进入设计优化的开放源码软件，并提供给工业界和研究界。

As space agencies and enterprises plan for future Mars missions with sequential spacecraft landings and large payload requirements, novel entry vehicles are currently being conceptualised. These spacecraft require control algorithms capable of achieving unprecedented landing precision, optimally managing thermal loads and propellent usage, while being robust to operate in highly uncertain atmospheric environments. With this application in mind, the research project aims to solve the Robust Optimal Control Problem (OCP) by faithfully including the uncertainties and nonlinearities of the model, achieving higher performance than current algorithms that use linear, time-varying basis functions for the feedback policy. The research will focus on the use of more general, neural networks as basis functions.Firstly, in the interest of solving optimal control problems - which can be posed as solving a system of differential algebraic equations (DAE) - an initial focus will be given to weighted residual methods, continuing previous work within the research group. Research will be carried in maturing this algorithm to be efficiently used for solving DAEs arising from optimal control problems. Despite the methods being general - able to solve a wide variety of OCPs (and DAEs) - special attention will be given to the spacecraft entry problem, targeting research towards the uncertain and nonlinear nature of the problem.Secondly, catering for the intrinsic uncertainty of the atmospheric environment, sensitive initial conditions, and vehicle design parameters of the problem in study, research will be carried in modelling these uncertainties. With an initial focus on polynomial chaos expansions and sample-based uncertainty as tools to explicitly represent, propagate and operate on the uncertainty of variables, which have been demonstrated to have better performance than traditional Monte Carlo methods. This is the backbone of the robustness in control algorithms this project aims to develop.Thirdly, given the significant nonlinear and non-smooth aspects of the spacecraft entry problem (e.g. three-dimensional attitude dynamics, supersonic and hypersonic effects, rocket staging and deployable structures, etc.) the use of nonlinear and non-smooth basis functions will be assessed. With a focus on neural networks, research will be carried on how they can be best used within a robust optimal control problem. An emphasis will be placed in including vehicle parameters (e.g. heat shield thickness, centre-of-mass position, actuator limits, etc.) in the dynamic optimisation process, yielding optimal spacecraft designs for a certain mission specification.This research project aims to output significant breakthroughs and improvements to current methods, theory and technology. Additionally, open-source software to solve differential equations, optimal control problems, trajectory optimisation problems, and overall spacecraft entry design optimisation will be developed and made available to industry and the research community.