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Computation of Reachable Sets Based on Hamilton-Jacobi-Bellman Equation with Running Cost Function

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posted on 01.08.2021, 10:39 by Wei LiaoWei Liao, Taotao Liang, Xiaohui Wei, Jizhou Lai, Qiaozhi Yin
A novel method for computing reachable sets is proposed in this paper. In the proposed method, a Hamilton-Jacobi-Bellman equation with running cost function is numerically solved and the reachable sets of different time horizons are characterized by a family of non-zero level sets of the solution of the Hamilton-Jacobi-Bellman equation. In addition to the classical reachable set, by setting different running cost functions and terminal conditions of the Hamilton-Jacobi-Bellman equation, the proposed method allows to compute more generalized reachable sets, which are referred to as cost-limited reachable sets. In order to overcome the difficulty of solving the Hamilton-Jacobi-Bellman equation caused by the discontinuity of the solution, a method based on recursion and grid interpolation is employed. At the end of this paper, some examples are taken to illustrate the validity and generality of the proposed method.

History

Email Address of Submitting Author

liaowei_nuaa@hotmail.com

ORCID of Submitting Author

0000-0003-2778-0572

Submitting Author's Institution

Nanjing University of Aeronautics and Astronautics

Submitting Author's Country

China