3 research outputs found
Interval Signal Temporal Logic from Natural Inclusion Functions
We propose an interval extension of Signal Temporal Logic (STL) called
Interval Signal Temporal Logic (I-STL). Given an STL formula, we consider an
interval inclusion function for each of its predicates. Then, we use minimal
inclusion functions for the and functions to recursively build an
interval robustness that is a natural inclusion function for the robustness of
the original STL formula. The resulting interval semantics accommodate, for
example, uncertain signals modeled as a signal of intervals and uncertain
predicates modeled with appropriate inclusion functions. In many cases,
verification or synthesis algorithms developed for STL apply to I-STL with
minimal theoretic and algorithmic changes, and existing code can be readily
extended using interval arithmetic packages at negligible computational
expense. To demonstrate I-STL, we present an example of offline monitoring from
an uncertain signal trace obtained from a hardware experiment and an example of
robust online control synthesis
A Toolbox for Fast Interval Arithmetic in numpy with an Application to Formal Verification of Neural Network Controlled Systems
In this paper, we present a toolbox for interval analysis in numpy, with an
application to formal verification of neural network controlled systems. Using
the notion of natural inclusion functions, we systematically construct interval
bounds for a general class of mappings. The toolbox offers efficient
computation of natural inclusion functions using compiled C code, as well as a
familiar interface in numpy with its canonical features, such as n-dimensional
arrays, matrix/vector operations, and vectorization. We then use this toolbox
in formal verification of dynamical systems with neural network controllers,
through the composition of their inclusion functions
Forward Invariance in Neural Network Controlled Systems
We present a framework based on interval analysis and monotone systems theory
to certify and search for forward invariant sets in nonlinear systems with
neural network controllers. The framework (i) constructs localized first-order
inclusion functions for the closed-loop system using Jacobian bounds and
existing neural network verification tools; (ii) builds a dynamical embedding
system where its evaluation along a single trajectory directly corresponds with
a nested family of hyper-rectangles provably converging to an attractive set of
the original system; (iii) utilizes linear transformations to build families of
nested paralleletopes with the same properties. The framework is automated in
Python using our interval analysis toolbox , in
conjunction with the symbolic arithmetic toolbox , demonstrated
on an -dimensional leader-follower system