Reachable Set Estimation and Safety Verification for Piecewise Linear Systems with Neural Network Controllers
It provides a formal verification method for safety-critical systems controlled by neural networks, but the approach is incremental and limited to piecewise linear systems with ReLU activations.
The paper develops a layer-by-layer method to compute output reachable sets for ReLU neural networks, enabling reachable set estimation and safety verification for piecewise linear systems with neural network controllers. The approach is demonstrated on a numerical example.
In this work, the reachable set estimation and safety verification problems for a class of piecewise linear systems equipped with neural network controllers are addressed. The neural network is considered to consist of Rectified Linear Unit (ReLU) activation functions. A layer-by-layer approach is developed for the output reachable set computation of ReLU neural networks. The computation is formulated in the form of a set of manipulations for a union of polytopes. Based on the output reachable set for neural network controllers, the output reachable set for a piecewise linear feedback control system can be estimated iteratively for a given finite-time interval. With the estimated output reachable set, the safety verification for piecewise linear systems with neural network controllers can be performed by checking the existence of intersections of unsafe regions and output reach set. A numerical example is presented to illustrate the effectiveness of our approach.