This research aims to develop a unified framework to compute in real-time optimal guidance solutions by merging two of the most promising technologies arisen over the last years, that is, pseudospectral optimal control, and convex optimization. The rationale for this choice can be found in the following motivations:
1. The former theory has very interesting properties, such as the quasi-exponential convergence to the true optimal solutions, and was already used to re-orient the International Space Station in 2006, leading to a save of about 1,000,000$ in terms of required propellant with respect to the previous methods.
2. Convex-optimization provides the technology to solve optimal control problems in real-time, a key feature for the future space systems, and computes the global optimum.
3. The two technologies are complementary as each method’s drawbacks are counterbalanced by the other method’s strengths, and their unification will yield an improvement of performance since the solutions will be optimal, in the sense of maximizing or minimizing a given criterion, while nowadays only sub-optimal schemes are available.
4. The research outcome will find applications in several industrial fields, leading to beneficial effects outside the space engineering field as well.
The hybrid approach will consist in transcribing the original optimal control problem by using pseoudospectral transcription, that is, by adopting differential, integral, and discretization operators coming from pseudospectral methods. The resulting discrete problem will be then posed in convex form, suitable for real-time applications.
The research will focus on the theoretical and algorithmic part, to be developed at the San Diego State University with Prof. Ping Lu during the first two years of program, while the third year will be spent at the German Aerospace Center, where the results will be implemented on a real-time architecture to show the maturity achieved by the proposed method.
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