Journal ArticleDOI
Entry Trajectory Optimization by Second-Order Cone Programming
Xinfu Liu,Zuojun Shen,Ping Lu +2 more
TLDR
This paper represents an attempt to apply second-order cone programming, a branch of convex optimization, to the class of highly nonlinear trajectory optimization problems in entry flight with a combination of successive linearization and relaxation techniques.Abstract:
Convex optimization has found wide applications in recent years due to its unique theoretical advantages and the polynomial-time complexity of state-of-the-art solution algorithms for convex programming This paper represents an attempt to apply second-order cone programming, a branch of convex optimization, to the class of highly nonlinear trajectory optimization problems in entry flight The foremost challenge in applying convex optimization in most aerospace engineering problems lies in the nonlinearity and nonconvexity of the problem Exclusive reliance on linearization does not always work well, as is the case in entry trajectory optimization This paper focuses on how to formulate realistic, highly constrained entry trajectory optimization problems in a fashion suitable to be solved by second-order cone programming with a combination of successive linearization and relaxation techniques Rigorous analysis is conducted to support the soundness of the approach Numerical demonstrations are provided toread more
Citations
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Journal ArticleDOI
Survey of convex optimization for aerospace applications
Xinfu Liu,Ping Lu,Binfeng Pan +2 more
TL;DR: 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 and various convexification techniques are reviewed that have been used to convexify the originally nonconvex aerospace problems.
Journal ArticleDOI
Constrained Trajectory Optimization for Planetary Entry via Sequential Convex Programming
Zhenbo Wang,Michael J. Grant +1 more
TL;DR: The highly nonlinear planetary-entry optimal control problem is formulated as a sequence of convex problems to facilitate rapid solution to avoid nonconvex control constraint.
Journal ArticleDOI
Pseudospectral Convex Optimization for Powered Descent and Landing
TL;DR: Over the last years, two new technologies to solve optimal-control problems were successfully developed: that is, pseudospectral optimal control and conveX optimization, with the former for solving convex optimization problems and the latter for solving pseudo-optimal control problems.
Journal ArticleDOI
Fuel-Optimal Rocket Landing with Aerodynamic Controls
TL;DR: In this article, the aerodynamic control and propulsion should be coordinated to realize fuel-optimal precise landing for a reusable rocket returning back to Earth, where aerodynamic forces are not negligible.
Journal ArticleDOI
Exact convex relaxation for optimal flight of aerodynamically controlled missiles
Xinfu Liu,Zuojun Shen,Ping Lu +2 more
TL;DR: To efficiently and reliably solve such a highly nonlinear (nonconvex) problem, it is presented how to obtain its convex relaxation and then proposed a regularization technique which is critical to guarantee the exactness of this relaxation.
References
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Book
Convex Optimization
Stephen Boyd,Lieven Vandenberghe +1 more
TL;DR: In this article, the focus is on recognizing convex optimization problems and then finding the most appropriate technique for solving them, and a comprehensive introduction to the subject is given. But the focus of this book is not on the optimization problem itself, but on the problem of finding the appropriate technique to solve it.
Journal ArticleDOI
On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
TL;DR: A comprehensive description of the primal-dual interior-point algorithm with a filter line-search method for nonlinear programming is provided, including the feasibility restoration phase for the filter method, second-order corrections, and inertia correction of the KKT matrix.
Proceedings ArticleDOI
YALMIP : a toolbox for modeling and optimization in MATLAB
TL;DR: Free MATLAB toolbox YALMIP is introduced, developed initially to model SDPs and solve these by interfacing eternal solvers by making development of optimization problems in general, and control oriented SDP problems in particular, extremely simple.
Book
Interior-Point Polynomial Algorithms in Convex Programming
TL;DR: This book describes the first unified theory of polynomial-time interior-point methods, and describes several of the new algorithms described, e.g., the projective method, which have been implemented, tested on "real world" problems, and found to be extremely efficient in practice.
Journal ArticleDOI
Applications of second-order cone programming
TL;DR: In this paper, an efficient primal-dual interior-point method for solving second-order cone programs (SOCP) is presented. But it is not a generalization of interior point methods for convex problems.