Data-driven synthesis of Robust Invariant Sets and Controllers

TL;DR

This paper introduces a data-driven method to identify uncertain LTI models and synthesize robust invariant sets and controllers for RMPC, ensuring stability and feasibility with less conservatism.

Contribution

It proposes a novel SDP-based approach to concurrently identify models and synthesize invariant sets and controllers, improving over sequential methods.

Findings

Less conservative invariant sets compared to sequential approaches

Guarantees recursive feasibility and stability of RMPC

Demonstrated effectiveness through a numerical example

Abstract

This paper presents a method to identify an uncertain linear time-invariant (LTI) prediction model for tube-based Robust Model Predictive Control (RMPC). The uncertain model is determined from a given state-input dataset by formulating and solving a Semidefinite Programming problem (SDP), that also determines a static linear feedback gain and corresponding invariant sets satisfying the inclusions required to guarantee recursive feasibility and stability of the RMPC scheme, while minimizing an identification criterion. As demonstrated through an example, the proposed concurrent approach provides less conservative invariant sets than a sequential approach.