Formulas for Data-driven Control: Stabilization, Optimality and Robustness
Provides a data-driven control framework for linear systems, eliminating the need for model identification, with extensions to nonlinear systems.
This paper derives a parametrization of linear feedback systems using persistently exciting data, enabling solution of stabilization, optimal control, and robustness problems via data-dependent Linear Matrix Inequalities without explicit system identification.
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.