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

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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.