Data-based stabilization of unknown bilinear systems with guaranteed basin of attraction
Andrea Bisoffi, Claudio De Persis, Pietro Tesi
Abstract
Motivated by the goal of having a building block in the design of direct data-driven controllers for nonlinear systems, we show how, for an unknown discrete-time bilinear system, the data collected in an offline open-loop experiment enable us to design a feedback controller and provide a guaranteed underapproximation of its basin of attraction. Both can be obtained by solving a linear matrix inequality for a fixed scalar parameter, and possibly iterating on different values of that parameter. The results of this data-based approach are compared with the ideal case when the model is known perfectly.
Topics & Concepts
Control theory (sociology)MathematicsBilinear interpolationNonlinear systemScalar (mathematics)Ideal (ethics)AttractionController (irrigation)Block (permutation group theory)Mathematical optimizationApplied mathematicsComputer scienceControl (management)LawArtificial intelligenceStatisticsQuantum mechanicsPolitical sciencePhilosophyLinguisticsGeometryPhysicsBiologyAgronomyControl Systems and IdentificationAdvanced Control Systems OptimizationFault Detection and Control Systems