Federated learning (FL) schemes allow multiple participants to collaboratively train neural networks without the need to directly share the underlying data. However, in early schemes, all participants eventually obtain the same model. Moreover, the aggregation is typically carried out by a third party, who obtains combined gradients or weights, which may reveal the model. These downsides underscore the demand for fair and privacy-preserving FL schemes. Here, collaborative fairness asks for individual model quality depending on the individual data contribution. Privacy is demanded with respect to any kind of data outsourced to the third party. Now, there already exist some approaches aiming for either fair or privacy-preserving FL and a few works even address both features. In our paper, we build upon these seminal works and present a novel, fair and privacy-preserving FL scheme. Our approach, which mainly relies on homomorphic encryption, stands out for exclusively using local gradients. This increases the usability in comparison to state-of-the-art approaches and thereby opens the door to applications in control.

Recently, it has been observed that finite impulse response controllers are an excellent basis for encrypted control, where privacy-preserving controller evaluations via special cryptosystems are the main focus. Beneficial properties of FIR filters are also well-known from digital signal processing, which makes them preferable over infinite impulse response filters in many applications. Their appeal extends to feedback control, offering design flexibility grounded solely on output measurements. However, designing FIR controllers is challenging, which motivates this work. To address the design challenge, we initially show that FIR controller designs for linear systems can equivalently be stated as static or dynamic output feedback problems. After focusing on the existence of stabilizing FIR controllers for a given plant, we tailor two common design approaches for output feedback to the case of FIR controllers. Unfortunately, it will turn out that the FIR characteristics add further restrictions to the LMI-based approaches. Hence, we finally turn to designs building on non-convex optimization, which provide satisfactory results for a selection of benchmark systems.