LMI-based Data-Driven Robust Model Predictive Control

Rawlings et al. provides an answer on how to design controllers directly (2017), Findeisen et al. (2007), Lucia et al. (2016)) has from data, where the system is implicitly represented via become a popular control scheme thanks to the ability of the Hankel matrix of measured trajectory. In short, the efficiently handling constraints and performance criteria lemma states that all trajectories of an controllable LTI as well as the coherent implementation of multiple hierarchical system can be represented by a finite set of its past trajectories, layers. The MPC scheme formulated as a semidefinite given that the past trajectories are generated by optimization problem in form of Linear Matrix a sufficiently exciting inputs. This idea has been investigated Inequalities (LMIs) is often used for some typical classes by De Persis and Tesi (2020), where the stabilizing of systems such as linear parameter-varying systems or feedback gain is designed by formulating the problem as Lur'e type systems, see for example, Kothare et al. (1996), LMIs without considering performance and constraints Böhm et al. (2009) and Nguyen et al. (2018). The reason guarantees, and Berberich et al. (2021), Coulson et al. for this is the formulated optimization problem is convex (2019) where this idea is used to develop a data-driven and can be efficiently solved.