10 research outputs found
Reachability Analysis for Neural Feedback Systems Using Regressive Polynomial Rule Inference
We present an approach to construct reachable set overapproxi- mations for continuous-time dynamical systems controlled using neural network feedback systems. Feedforward deep neural net- works are now widely used as a means for learning control laws through techniques such as reinforcement learning and data-driven predictive control. However, the learning algorithms for these net- works do not guarantee correctness properties on the resulting closed-loop systems. Our approach seeks to construct overapproxi- mate reachable sets by integrating a Taylor model-based flowpipe construction scheme for continuous differential equations with an approach that replaces the neural network feedback law for a small subset of inputs by a polynomial mapping. We generate the polynomial mapping using regression from input-output sam- ples. To ensure soundness, we rigorously quantify the gap between the output of the network and that of the polynomial model. We demonstrate the effectiveness of our approach over a suite of bench- mark examples ranging from 2 to 17 state variables, comparing our approach with alternative ideas based on range analysis
NNV: The Neural Network Verification Tool for Deep Neural Networks and Learning-Enabled Cyber-Physical Systems
This paper presents the Neural Network Verification (NNV) software tool, a
set-based verification framework for deep neural networks (DNNs) and
learning-enabled cyber-physical systems (CPS). The crux of NNV is a collection
of reachability algorithms that make use of a variety of set representations,
such as polyhedra, star sets, zonotopes, and abstract-domain representations.
NNV supports both exact (sound and complete) and over-approximate (sound)
reachability algorithms for verifying safety and robustness properties of
feed-forward neural networks (FFNNs) with various activation functions. For
learning-enabled CPS, such as closed-loop control systems incorporating neural
networks, NNV provides exact and over-approximate reachability analysis schemes
for linear plant models and FFNN controllers with piecewise-linear activation
functions, such as ReLUs. For similar neural network control systems (NNCS)
that instead have nonlinear plant models, NNV supports over-approximate
analysis by combining the star set analysis used for FFNN controllers with
zonotope-based analysis for nonlinear plant dynamics building on CORA. We
evaluate NNV using two real-world case studies: the first is safety
verification of ACAS Xu networks and the second deals with the safety
verification of a deep learning-based adaptive cruise control system
Reach-SDP: Reachability Analysis of Closed-Loop Systems with Neural Network Controllers via Semidefinite Programming
There has been an increasing interest in using neural networks in closed-loop
control systems to improve performance and reduce computational costs for
on-line implementation. However, providing safety and stability guarantees for
these systems is challenging due to the nonlinear and compositional structure
of neural networks. In this paper, we propose a novel forward reachability
analysis method for the safety verification of linear time-varying systems with
neural networks in feedback interconnection. Our technical approach relies on
abstracting the nonlinear activation functions by quadratic constraints, which
leads to an outer-approximation of forward reachable sets of the closed-loop
system. We show that we can compute these approximate reachable sets using
semidefinite programming. We illustrate our method in a quadrotor example, in
which we first approximate a nonlinear model predictive controller via a deep
neural network and then apply our analysis tool to certify finite-time
reachability and constraint satisfaction of the closed-loop system