Geodesy

Quantum mechanics

Algorithm

Benchmark (surveying)

Feedforward neural network

Engineering

Control engineering

Soundness

Computer science

Polynomial

Reachability

Correctness

Physics

Mathematics

Geography

Feed forward

Mathematical analysis

Artificial intelligence

Dynamical systems theory

Programming language

Artificial neural network

We present an approach to construct reachable set overapproximations for continuous-time dynamical systems controlled using neural network feedback systems. Feedforward deep neural networks 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 networks do not guarantee correctness properties on the resulting closed-loop systems. Our approach seeks to construct overapproximate 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 samples. 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 benchmark examples ranging from 2 to 17 state variables, comparing our approach with alternative ideas based on range analysis.

Reachability analysis for neural feedback systems using regressive polynomial rule inference