Abstract
Abstract In this paper, we consider the problem of computing multidimensional interval controlled invariants for nonlinear input-affine systems. We first present sufficient conditions for an interval to be controlled invariant. Then, we introduce the concept of local framers, based on which we present a sound algorithm to compute interval controlled invariants. Finally, we show how the proposed framework makes it possible to provide safety guarantees when using deep neural networks, either as a model or a controller of nonlinear systems. Illustrative examples are provided showing the merits of the proposed approach and its scalability properties.
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