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Computation of Reachable Sets Based on Hamilton-Jacobi-Bellman Equation with Running Cost Function
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  • Wei Liao ,
  • Taotao Liang ,
  • Xiaohui Wei ,
  • Jizhou Lai ,
  • Qiaozhi Yin
Wei Liao
Nanjing University of Aeronautics and Astronautics

Corresponding Author:[email protected]

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Taotao Liang
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Xiaohui Wei
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Jizhou Lai
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Qiaozhi Yin
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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 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.