Limited-complexity controller tuning: A set membership data-driven approach

Data-driven tuning is an alternative to model-based controller design where controllers are directly identified from data, avoiding a plant identification step. In this paper, an approach to tune limited-complexity controllers from data for linear systems is proposed. The controller is parametrized as a linear combination of a large set of basis functions and the proposed algorithm allows to select a sparse subset of bases, guaranteeing a bounded approximation error. A feasibility condition allows to adjust the trade-off between accuracy and sparsity. The controller design is performed by solving a set of linear programming problems, allowing to handle large data-sets. The proposed strategy is evaluated by means of a Monte-Carlo simulation experiment on a flexible transmission benchmark model. Results show that the proposed solution offers similar results than previous approaches for large data-sets, requiring less adjustable parameters. However, for reduced data-sets, the presented algorithm shows better performance than the compared approaches.