Data-Driven Control Design with LMIs and Dynamic Programming

TL;DR

This paper introduces data-driven control design methods for unknown LTI systems using LMIs and dynamic programming, ensuring stability and optimality through efficient data collection and exploration strategies.

Contribution

It presents novel data collection schemes, data-driven LMIs for control design, and convergence-guaranteed dynamic programming algorithms for unknown systems.

Findings

Data collection schemes improve data validity with more data.

Data-driven LMIs enable stabilization and LQR control.

Convergence guarantees for dynamic programming algorithms.

Abstract

The goal of this paper is to develop data-driven control design and evaluation strategies based on linear matrix inequalities (LMIs) and dynamic programming. We consider deterministic discrete-time LTI systems, where the system model is unknown. We propose efficient data collection schemes from the state-input trajectories together with data-driven LMIs to design state-feedback controllers for stabilization and linear quadratic regulation (LQR) problem. In addition, we investigate theoretically guaranteed exploration schemes to acquire valid data from the trajectories under different scenarios. In particular, we prove that as more and more data is accumulated, the collected data becomes valid for the proposed algorithms with higher probability. Finally, data-driven dynamic programming algorithms with convergence guarantees are then discussed.