Virtual reference feedback tuning with robustness constraints: A swarm intelligence solution

The simplified modeling of a complex system allied with a low-order controller structure can lead to poor closed-loop performance and robustness. A feasible solution is to avoid the necessity of a model by using data for the controller design. The Virtual Reference Feedback Tuning (VRFT) is a data-driven design method that only requires a single batch of data and solves a reference tracking problem, although with no guarantee of robustness. In this work, the inclusion of an $\mathcal{H}_{\infty}$ robustness constraint to the VRFT cost function is addressed. The estimation of the $\mathcal{H}_{\infty}$ norm of the sensitivity transfer function is extended to maintain the one-shot characteristic of the VRFT. Swarm intelligence algorithms are used to solve the non-convex cost function. The proposed method is applied in two real-world inspired problems with four different swarm intelligence algorithms, which are compared with each other through a Monte Carlo experiment of 50 executions. The obtained results are satisfactory, achieving the desired robustness criteria.