From Data to Predictive Control: A Framework for Stochastic Linear Systems with Output Measurements

We introduce data to predictive control, D2PC, a framework to facilitate the design of robust and predictive controllers from data. The proposed framework is designed for discrete-time stochastic linear systems with output measurements and provides a principled design of a predictive controller based on data. The framework builds on a parameter identification method based on the Expectation-Maximization algorithm, which incorporates pre-defined structural constraints. An asymptotic approximation is leveraged to quantify the uncertainty in the parameter estimates. As the main contributions, a robust control and predictive control design are proposed tailored to the uncertainty characterization resulting from the identification. In particular, a strategy to synthesize robust dynamic output-feedback controllers is presented. Furthermore, a predictive control scheme that guarantees recursive feasibility and satisfaction of chance constraints is developed. This framework marks a significant advancement in integrating data-driven models into robust and predictive control designs. We demonstrate the efficacy of D2PC through a numerical example involving a $10$-dimensional spring-mass-damper system.