A swarm intelligence-based robust solution for Virtual Reference Feedback Tuning

This work proposes the inclusion of an $\mathcal{H}_{\infty}$ robustness constraint to the Virtual Reference Feedback Tuning (VRFT) cost function, which is solved by metaheuristic optimization with only a single batch of data (one-shot). The $\mathcal{H}_{\infty}$ norm of the sensitivity function is estimated in a data-driven fashion, based on the regularized estimation of the system's impulse response. Four different swarm intelligence algorithms are chosen to be evaluated and compared at the optimization problem. Two real-world based examples are used to illustrate the proposed method through a Monte Carlo experiment with 50 runs. To compare the swarm intelligence algorithms to each other, 50 search agents have been adopted, with a maximum number of iterations of 100. For all cases, the Improved Grey Wolf Optimizer (I-GWO) algorithm presented the least number of outliers and faster convergence, with the closest dynamic behavior to the desired, satisfying the imposed robustness constraint with lower fitness than other tested algorithms.