Discrete-time model-based output regulation of fluid flow systems

Discrete-time output observers for boundary control systems

“…A similar idea has been recently used by Dubljevic and Humaloja (2020) as well as Xie et al (2021), where the discrete-time infinite-dimensional models, obtained by the Cayley transformation, have been used to develop control algorithms for continuous-time infinite-dimensional state space plant models. We emphasize that in our paper we start with a continuous-time plant model in the form of a boundary input-output system in contrast to the state space description investigated by Dubljevic and Humaloja (2020) or Xie et al (2021). Our choice of the plant model shows the advantage of using the resolvent R(μ) and the Green map G(μ) in the discrete-time model.…”

“…This way of simplifying an infinite-dimensional control model is already known in the literature but interest of researchers has been rather focused on system theoretic properties preserved under the Cayley transformation and not on using such models in developing control and observation algorithms (e.g., Ober and Montgomery-Smith, 1990;Curtain and Oostveen, 1997;Guo and Zwart, 2006;Havu and Malinen, 2007). However, recently this approach has been also successfully used by Dubljevic and Humaloja (2020) to handle model predictive control of infinite-dimensional systems and by Xie et al (2021) to handle output regulation of fluid flow systems. The idea was also involved in the discrete-time stabilization problem of a heat equation by Mitkowski et al (2017).…”