1,840 research outputs found
Safety Verification of Neural Feedback Systems Based on Constrained Zonotopes
Artificial neural networks (ANNs) have been utilized in many feedback control
systems and introduced new challenges regarding the safety of the system. This
paper considers the problem of verifying whether the trajectories of a system
with a feedforward neural network (FNN) controller can avoid unsafe regions,
using a constrained zonotope-based reachability analysis approach. FNNs with
the rectified linear unit activation function are considered in this work. A
novel set-based method is proposed to compute both exact and over-approximated
reachable sets for linear discrete-time systems with FNN controllers, and
linear program-based sufficient conditions are presented to certify the safety
of the neural feedback systems. Reachability analysis and safety verification
for neural feedback systems with nonlinear models are also considered. The
computational efficiency and accuracy of the proposed method are demonstrated
by two numerical examples where a comparison with state-of-the-art methods is
also provided.Comment: 8 pages, 4 figure
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
Automated Reachability Analysis of Neural Network-Controlled Systems via Adaptive Polytopes
Over-approximating the reachable sets of dynamical systems is a fundamental
problem in safety verification and robust control synthesis. The representation
of these sets is a key factor that affects the computational complexity and the
approximation error. In this paper, we develop a new approach for
over-approximating the reachable sets of neural network dynamical systems using
adaptive template polytopes. We use the singular value decomposition of linear
layers along with the shape of the activation functions to adapt the geometry
of the polytopes at each time step to the geometry of the true reachable sets.
We then propose a branch-and-bound method to compute accurate
over-approximations of the reachable sets by the inferred templates. We
illustrate the utility of the proposed approach in the reachability analysis of
linear systems driven by neural network controllers
Output Reachable Set Estimation and Verification for Multi-Layer Neural Networks
In this paper, the output reachable estimation and safety verification
problems for multi-layer perceptron neural networks are addressed. First, a
conception called maximum sensitivity in introduced and, for a class of
multi-layer perceptrons whose activation functions are monotonic functions, the
maximum sensitivity can be computed via solving convex optimization problems.
Then, using a simulation-based method, the output reachable set estimation
problem for neural networks is formulated into a chain of optimization
problems. Finally, an automated safety verification is developed based on the
output reachable set estimation result. An application to the safety
verification for a robotic arm model with two joints is presented to show the
effectiveness of proposed approaches.Comment: 8 pages, 9 figures, to appear in TNNL
- …