Encrypted dynamic control with unlimited operating time via FIR filters

Encrypted control enables confidential controller evaluations in cloud-based or networked control systems. From a technical point of view, an encrypted controller is a modified control algorithm that is capable of computing encrypted control actions based on encrypted system outputs. Unsurprisingly, encrypted implementations of controllers using, e.g., homomorphic cryptosystems entail new design challenges. For instance, in order to avoid overflow or high computational loads, only a finite number of operations should be carried out on encrypted data. Clearly, this guideline is hard to satisfy for dynamic controllers due to their recursive nature. To enable an unlimited operating time, existing implementations thus rely on external "refreshments" of the controller state, internal refreshments using bootstrapping, or recurring controller resets. We show in this paper that simple FIR filter-based controllers allow to overcome many drawbacks of the existing approaches. In fact, since FIR filters consider only a finite amount of the most recent input data, the recursion issue is immediately solved and controller refreshments or resets are no longer required. Moreover, well-designed FIR filters are often less complex than and equally effective as IIR controllers.