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Computation of Controlled Invariants for Nonlinear Systems: Application to Safe Neural Networks Approximation and Control⁎A. Saoud and R. G. Sanfelice are with Department of Electrical and Computer Engineering, University of California, Santa Cruz. This research has been partially supported by NSF Grants no. ECS-1710621, CNS-1544396, and CNS-2039054, by AFOSR Grants no. FA9550-19-1-0053, FA9550-19-1-0169, and FA9550-20-1-0238, and by CITRIS and the Banatao Institute at the University of California. Issue 5 (2021)
Record Type:
Journal Article
Title:
Computation of Controlled Invariants for Nonlinear Systems: Application to Safe Neural Networks Approximation and Control⁎A. Saoud and R. G. Sanfelice are with Department of Electrical and Computer Engineering, University of California, Santa Cruz. This research has been partially supported by NSF Grants no. ECS-1710621, CNS-1544396, and CNS-2039054, by AFOSR Grants no. FA9550-19-1-0053, FA9550-19-1-0169, and FA9550-20-1-0238, and by CITRIS and the Banatao Institute at the University of California. Issue 5 (2021)
Main Title:
Computation of Controlled Invariants for Nonlinear Systems: Application to Safe Neural Networks Approximation and Control⁎A. Saoud and R. G. Sanfelice are with Department of Electrical and Computer Engineering, University of California, Santa Cruz. This research has been partially supported by NSF Grants no. ECS-1710621, CNS-1544396, and CNS-2039054, by AFOSR Grants no. FA9550-19-1-0053, FA9550-19-1-0169, and FA9550-20-1-0238, and by CITRIS and the Banatao Institute at the University of California.
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.