Survey of convex optimization for aerospace applications

Abstract

Convex optimization is a class of mathematical programming problems with polynomial complexity for which state-of-the-art, highly efficient numerical algorithms with predeterminable computational bounds exist. Computational efficiency and tractability in aerospace engineering, especially in guidance, navigation, and control (GN&C), are of paramount importance. With theoretical guarantees on solutions and computational efficiency, convex optimization lends itself as a very appealing tool. Coinciding the strong drive toward autonomous operations of aerospace vehicles, convex optimization has seen rapidly increasing utility in solving aerospace GN&C problems with the potential for onboard real-time applications. This paper attempts to provide an overview on the problems to date in aerospace guidance, path planning, and control where convex optimization has been applied. Various convexification techniques are reviewed that have been used to convexify the originally nonconvex aerospace problems. Discussions on how to ensure the validity of the convexification process are provided. Some related implementation issues will be introduced as well.

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Acknowledgements

The author at Beijing Institute of Technology gratefully acknowledges the support to this work by the National Natural Science Foundation of China (Grant No. 61603017).

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Correspondence to Xinfu Liu.

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Xinfu Liu received his B.E. degree in the Department of Automation, Central South University, Changsha, China, in 2008, and Ph.D. degree in aerospace engineering from Iowa State University, Ames, USA, in 2013. From 2013 to 2016 he was a postdoctoral research associate at Beihang University, Beijing, China. Since 2016, he has been an associate professor in the School of Aerospace Engineering, Beijing Institute of Technology, Beijing, China. His research interests are in optimal control, autonomous trajectory planning of flight vehicles, and convex optimization and its applications.

Binfeng Pan is an associate professor in the School of Astronautics, Northwestern Polytechnical University (NPU). He received his M.S. and Ph.D. degrees in aerospace engineering from NPU in 2007 and 2010 respectively. His research interests are in the trajectory optimization, onboard guidance and control algorithms design.

Ping Lu received his baccalaureate degree from the Beijing Institute of Aeronautics, and Ph.D. degree in aerospace engineering from the University of Michigan. He was on the faculty of aerospace engineering at Iowa State University from 1990 to 2016 where his last position was professor. He joined the San Diego State University in 2016 to be a professor and the Chair of the Aerospace Engineering Department. His research interests and expertise are in aerospace guidance, flight control, and autonomous trajectory planning and optimization. Prof. Lu was the recipient of the prestigious American Institute of Aeronautics and Astronautics (AIAA) Mechanics and Control of Flight Award in 2008, “for contributions in advanced guidance algorithms for entry and ascent fligh”. He is an AIAA Fellow, and the Editor-in-Chief of Journal of Guidance, Control, and Dynamics.

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Liu, X., Lu, P. & Pan, B. Survey of convex optimization for aerospace applications. Astrodyn 1, 23–40 (2017). https://doi.org/10.1007/s42064-017-0003-8

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Keywords

  • convex optimization
  • optimal control
  • convexification
  • convex relaxation