Data-driven Linear Quadratic Regulation via Semidefinite Programming

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.Comment: Accepted for publication in the IFAC World Congress 202

Formulas for Data-driven Control: Stabilization, Optimality and Robustness

In a paper by Willems and coauthors it was shown that persistently exciting data can be used to represent the input-output behavior of a linear system. Based on this fundamental result, we derive a parametrization of linear feedback systems that paves the way to solve important control problems using data-dependent Linear Matrix Inequalities only. The result is remarkable in that no explicit system's matrices identification is required. The examples of control problems we solve include the state and output feedback stabilization, and the linear quadratic regulation problem. We also discuss robustness to noise-corrupted measurements and show how the approach can be used to stabilize unstable equilibria of nonlinear systems.Comment: Revised version of the paper "On Persistency of Excitation and Formulas for Data-driven Control". Abridged version to appear in the 58th IEEE Conference on Decision and Control, Nice, France, 2019. First submitted on 15 March 201