Encrypted dynamic controllers that operate for an unlimited time have been a challenging subject of research. The fundamental difficulty is the accumulation of errors and scaling factors in the internal state during operation. Bootstrapping, a technique commonly employed in fully homomorphic cryptosystems, can be used to avoid overflows in the controller state but can potentially introduce significant numerical errors.In this paper, we analyze dynamic encrypted control with explicit consideration of bootstrapping. By recognizing the bootstrapping errors occurring in the controller's state as an uncertainty in the robust control framework, we can provide stability and performance guarantees for the whole encrypted control system. Further, the conservatism of the stability and performance test is reduced by using a lifted version of the control system.

Model-based algorithms are deeply rooted in modern control and systems theory. However, they usually come with a critical assumption -access to an accurate model of the system. In practice, models are far from perfect. Even precisely tuned estimates of unknown parameters will deteriorate over time. Therefore, it is essential to detect the change to avoid suboptimal or even dangerous behavior of a control system. We propose to combine statistical tests with dedicated parameter filters that track unknown system parameters from state data. These filters yield point estimates of the unknown parameters and, further, an inherent notion of uncertainty. When the point estimate leaves the confidence region, we trigger active learning experiments. We update models only after enforcing a sufficiently small uncertainty in the filter. Thus, models are only updated when necessary and statistically significant while ensuring guaranteed improvement, which we call event-triggered learning. We validate the proposed method in numerical simulations of a DC motor in combination with model predictive control.

Encrypted control systems allow to evaluate feedback laws on external servers without revealing private information about state and input data, the control law, or the plant. While there are a number of encrypted control schemes available for linear feedback laws, only few results exist for the evaluation of more general control laws. Recently, an approach to encrypted polynomial control was presented, relying on two-party secret sharing and an inter-server communication protocol using homomorphic encryption. As homomorphic encryptions are much more computationally demanding than secret sharing, they make up for a tremendous amount of the overall computational demand of this scheme. For this reason, in this paper, we investigate schemes for secure polynomial control based solely on secret sharing. We introduce a novel secure three-party control scheme based on three-party computation. Further, we propose a novel n-party control scheme to securely evaluate polynomial feedback laws of arbitrary degree without inter-server communication. The latter property makes it easier to realize the necessary requirement regarding non-collusion of the servers, with which perfect security can be guaranteed. Simulations suggest that the presented control schemes are many times less computationally demanding than the two-party scheme mentioned above.