Computation of Controlled Invariants for Nonlinear Systems: Application to Safe Neural Networks Approximation and Control

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. Copyright (C) 2021 The Authors.