One-Step Safe Neural Network Supported Control

Controlling systems that are subject to state and input constraints using either neural networks-based or neural network-supported controllers is challenging. We focus on the neural network output layer to enforce constraint satisfaction and guarantees such as set invariance. In particular, we restrict the neural network output to a suitable set of control inputs that enables the flexible choice of guarantees depending on the requirements and the accessible model. The main contribution is the formal derivation of such a set for linear time-invariant systems. The result is a computationally efficient neural network output function that guarantees set inclusion without the requirement of adjusting a possibly existing baseline controller. Furthermore, we provide a numerical example to highlight the efficiency of the method as well as a detailed discussion of the results.