Data-driven Linear Quadratic Regulation via Semidefinite Programming

TL;DR

This paper presents a data-driven method for solving finite-horizon linear quadratic regulation problems with unknown dynamics, using input-state data and semidefinite programming to compute optimal control laws.

Contribution

It introduces a novel data-driven approach that leverages persistently exciting data and semidefinite programming to find optimal control without knowing system dynamics.

Findings

Successfully computes optimal control laws from data

Demonstrates effectiveness through numerical examples

Applicable to systems with unknown dynamics

Abstract

This paper studies the finite-horizon linear quadratic regulation problem where the dynamics of the system are assumed to be unknown and the state is accessible. Information on the system is given by a finite set of input-state data, where the input injected in the system is persistently exciting of a sufficiently high order. Using data, the optimal control law is then obtained as the solution of a suitable semidefinite program. The effectiveness of the approach is illustrated via numerical examples.