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Capture basin approximation using interval analysis. (English) Zbl 1225.93057
Summary: This paper proposes a new approach for computing the capture basin $$\mathbf C$$ of a target $$\mathbf T$$. The capture basin corresponds to the set of initial state vectors such that the target could be reached in finite time via an appropriate control input, before possibly leaving the target. Whereas classical capture basin characterization does not provide any guarantee on the set of state vectors that belong to the capture basin, interval analysis and guaranteed numerical integration allow us to avoid any indetermination. We present an algorithm that is able to provide guaranteed approximation of the inner $$\mathbf C^-$$ and the outer $$\mathbf C^+$$ of the capture basin, such that $$\mathbf C^-\subseteq \mathbf C\subset \mathbf C^+$$. In order to illustrate the principle and the efficiency of the approach, a testcase on the ’car on the hill’ problem is provided.

##### MSC:
 93C10 Nonlinear systems in control theory 93C15 Control/observation systems governed by ordinary differential equations 65G40 General methods in interval analysis
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