Low-cost Data-Driven Predictive Stabilization of Unknown LTI Systems: Two LMI Approaches

Abstract

In this paper, we address data-driven predictive control of Linear Time-Invariant (LTI) systems. Specifically, we demonstrate the direct learning of predictive laws from data, eliminating the need for system identification prior to control. Indeed, a data-based system representation, which provides a more accurate description of the original system, is constructed to replace the traditional model for predicting future behaviors. This approach helps to reduce the computational burden. Furthermore, two separate techniques for data-driven predictive control are presented for stabilizing an unknown LTI system. In each approach, a state feedback control law is formulated at every time step to optimize an infinite horizon objective function with the goal of stabilizing the unknown system based on the available data. We exemplify our findings through two numerical examples, emphasizing key features of our approaches. © 2024 IEEE.