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

TL;DR

This paper presents D2PC, a comprehensive data-driven framework for designing robust, predictive controllers for stochastic linear systems with output measurements, integrating parameter estimation, uncertainty quantification, and control synthesis.

Contribution

It introduces a novel framework combining data-based parameter identification, uncertainty quantification, and robust predictive control for stochastic linear systems.

Findings

Successful application to a 10-dimensional spring-mass-damper system

Guarantees recursive feasibility and chance constraint satisfaction

Provides asymptotically correct uncertainty bounds

Abstract

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 starts with a parameter identification method based on the Expectation-Maximization algorithm, which incorporates pre-defined structural constraints. Additionally, we provide an asymptotically correct method to quantify uncertainty in parameter estimates. Next, we develop a strategy to synthesize robust dynamic output-feedback controllers tailored to the derived uncertainty characterization. Finally, we introduce a predictive control scheme that guarantees recursive feasibility and satisfaction of chance constraints. This framework marks a significant advancement in integrating data into robust and predictive control schemes. We demonstrate the efficacy of D2PC through a numerical example involving a 10-dimensional spring-mass-damper system.