Automatic Basis Function Generation for Grid-Based Linear Parameter-Varying Control Synthesis

Control design for Linear Parameter-Varying (LPV) systems based on linear matrix inequalities requires the designer to provide basis functions. Usually, these basis functions are picked based on the intuition of how the system dynamics depends on its scheduling parameters. This paper presents a novel method of obtaining these basis functions from the state-space data of grid-based LPV systems in an automatic fashion. The method yields a small number of basis functions that often achieve better control performance and reduced computation time for control synthesis compared to their handpicked counterparts. This is accomplished by applying the tensor product model transformation to the tensor formed from the state-space matrices of the grid-based LPV system. Our MATLAB implementation of the algorithm described in this paper is open-source and available on GitHub.