  Modern automation systems rely on closed loop control, wherein a controller
interacts with a controlled process, based on observations. These systems are
increasingly complex, yet most controllers are linear
Proportional-Integral-Derivative (PID) controllers. PID controllers perform
well on linear and near-linear systems but their simplicity is at odds with the
robustness required to reliably control complex processes. Modern machine
learning offers a way to extend PID controllers beyond their linear
capabilities by using neural networks. However, such an extension comes at the
cost of losing stability guarantees and controller interpretability. In this
paper, we examine the utility of extending PID controllers with recurrent
neural networks-namely, General Dynamic Neural Networks (GDNN); we show that
GDNN (neural) PID controllers perform well on a range of control systems and
highlight how they can be a scalable and interpretable option for control
systems. To do so, we provide an extensive study using four benchmark systems
that represent the most common control engineering benchmarks. All control
benchmarks are evaluated with and without noise as well as with and without
disturbances. The neural PID controller performs better than standard PID
control in 15 of 16 tasks and better than model-based control in 13 of 16
tasks. As a second contribution, we address the lack of interpretability that
prevents neural networks from being used in real-world control processes. We
use bounded-input bounded-output stability analysis to evaluate the parameters
suggested by the neural network, thus making them understandable. This
combination of rigorous evaluation paired with better interpretability is an
important step towards the acceptance of neural-network-based control
approaches. It is furthermore an important step towards interpretable and
safely applied artificial intelligence.
