Data-Driven Sub-Optimal LQ Regulator for Linear Input-Delay Systems based on Informativity

TL;DR

This paper introduces a data-driven method for designing sub-optimal LQ controllers for linear input-delay systems using noisy data, leveraging informativity and convex optimization.

Contribution

It develops an LMI-based synthesis approach that guarantees LQ performance for all models consistent with the data, addressing input delays.

Findings

The method effectively synthesizes controllers from noisy data.

Numerical simulations confirm the approach's effectiveness.

Trade-offs between performance and data uncertainty are analyzed.

Abstract

This paper proposes a novel informativity-based data-driven synthesis method for a sub-optimal linear quadratic (LQ) regulator for linear input-delay systems from noisy input-state data. Exploiting the augmented state structure of input-delay systems with a known delay length, we derive a linear matrix inequality (LMI) condition for the data-driven synthesis of the augmented state-feedback controller that achieves a prescribed LQ performance level for every plant model consistent with the data. The proposed LMI condition enables efficient controller synthesis via convex optimization. Numerical simulations demonstrate the effectiveness of the proposed method. The trade-off between the achievable LQ performance and the uncertainty in the data is also clarified through a numerical example.