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In this work, the reachable set estimation and safety verification problemsfor a class of piecewise linear systems equipped with neural networkcontrollers are addressed. The neural network is considered to consist ofRectified Linear Unit (ReLU) activation functions. A layer-by-layer approach isdeveloped for the output reachable set computation of ReLU neural networks. Thecomputation is formulated in the form of a set of manipulations for a union ofpolytopes. Based on the output reachable set for neural network controllers,the output reachable set for a piecewise linear feedback control system can beestimated iteratively for a given finite-time interval. With the estimatedoutput reachable set, the safety verification for piecewise linear systems withneural network controllers can be performed by checking the existence ofintersections of unsafe regions and output reach set. A numerical example ispresented to illustrate the effectiveness of our approach.

Reachable Set Estimation and Safety Verification for Piecewise Linear Systems with Neural Network Controllers