Backward Reachability Analysis for Nonlinear Dynamical Systems via Pseudospectral Method
- Title
- Backward Reachability Analysis for Nonlinear Dynamical Systems via Pseudospectral Method
- Author
- 문준
- Keywords
- Backward reachable set; nonlinear programming; optimal control; pseudospectral method
- Issue Date
- 2021-02
- Publisher
- INST CONTROL ROBOTICS & SYSTEMS
- Citation
- INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND SYSTEMS, v. 19, no. 2, page. 575-586
- Abstract
- In this paper, we propose a new approach to solving the backward reachability problem for nonlinear dynamical systems. Previously, this class of problems has been studied within frameworks of optimal control and zero-sum differential games, where a backward reachable set can be expressed as the zero sublevel set of the value function that can be characterized by solving the Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE). In many cases, however, a high computational cost is incurred in numerically solving such HJB PDEs due to the curse of dimensionality. We use the pseudospectral method to convert the associated optimal control problem into nonlinear programs (NLPs). We then show that the zero sublevel set obtained by the optimal cost of the NLP is the corresponding backward reachable set. Note that our approach does not require solving complex HJB PDEs. Therefore, it can reduce computation time and handle high-dimensional dynamical systems, compared with the numerical software package developed by I. Mitchell, which has been used widely in the literature to obtain backward reachable sets by solving HJB equations. We provide several examples to validate the effectiveness of the proposed approach.
- URI
- https://link.springer.com/article/10.1007/s12555-019-0705-1https://repository.hanyang.ac.kr/handle/20.500.11754/176330
- ISSN
- 1598-6446; 2005-4092
- DOI
- 10.1007/s12555-019-0705-1
- Appears in Collections:
- COLLEGE OF ENGINEERING[S](공과대학) > ELECTRICAL AND BIOMEDICAL ENGINEERING(전기·생체공학부) > Articles
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