A Unified Optimization Algorithm for Bang-Bang Optimal Control

Abstract

This paper proposes a unified algorithm based on iterative second-order cone programming (SOCP) to solve bang-bang optimal control problems. For a bang-bang optimal control problem, the control values are constrained at the upper or lower bound. We first formulate the bang-bang optimal control problem as a nonconvex quadratically constrained quadratic programming (QCQP) problem by expressing the bang-bang control profiles as quadratic equality constraints. Then an iterative algorithm is proposed to solve nonconvex QCQPs, where each iteration is formulated as a SOCP problem. To obtain robust convergence of the proposed iterative algorithm under random initial guess, a multi-stage framework, combined with the relaxation technique, is introduced. To be specific, in the first stage, the QCQP problem is reformulated, where the terminal equality constraints are removed and handled as weighted penalty terms in the objective function. Together with the relaxed bang-bang constraints, the reformulated problem in the first stage is solved via the iterative SOCP and its solution is used as the initial guess for the second stage. In the second stage, the bang-bang constraints of the original problem are considered to obtain the final solution. Finally, the proposed algorithm is applied to the fuel-optimal powered descent guidance problem, and the effectiveness and robustness of the proposed algorithm are verified via numerical simulations.

Department(s)

Mechanical and Aerospace Engineering

International Standard Book Number (ISBN)

978-162410631-6

Document Type

Article - Conference proceedings

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2024 American Institute of Aeronautics and Astronautics, All rights reserved.

Publication Date

01 Jan 2022

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