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.

翻译：近年来，有限脉冲响应控制器被证明是实现加密控制的理想基础架构，其核心关注点在于通过特殊密码系统实现隐私保护的控制器运算。FIR滤波器在数字信号处理领域的优良特性已广为人知，这使得其在众多应用场景中比无限脉冲响应滤波器更具优势。这种优势同样延伸至反馈控制领域，为仅基于输出测量的控制系统提供了灵活的设计空间。然而，FIR控制器的设计本身具有挑战性，这构成了本研究的动机。为应对设计挑战，我们首先证明线性系统的FIR控制器设计可以等价表述为静态或动态输出反馈问题。在聚焦于给定被控对象存在稳定性FIR控制器的条件后，我们将两种常见的输出反馈设计方法适配于FIR控制器场景。遗憾的是，FIR特性将在线性矩阵不等式方法中引入额外约束。因此，我们最终转向基于非凸优化的设计方案，该方案在多个基准系统测试中取得了令人满意的结果。