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Electrical Engineering and Systems Science > Systems and Control

arXiv:2107.11941 (eess)
[Submitted on 26 Jul 2021 (v1), last revised 17 May 2022 (this version, v3)]

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

Authors:Weiwei Liao, Tao Liang
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Abstract:A novel method for computing reachable sets is proposed in this paper. In the proposed method, a Hamilton-Jacobi-Bellman equation with running cost functionis 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 conditionsof 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.
Subjects: Systems and Control (eess.SY); Optimization and Control (math.OC)
Cite as: arXiv:2107.11941 [eess.SY]
  (or arXiv:2107.11941v3 [eess.SY] for this version)
  https://doi.org/10.48550/arXiv.2107.11941

Submission history

From: Wei Liao [view email]
[v1] Mon, 26 Jul 2021 03:30:08 UTC (8,261 KB)
[v2] Wed, 16 Feb 2022 07:18:05 UTC (8,435 KB)
[v3] Tue, 17 May 2022 01:53:54 UTC (8,262 KB)
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