Bayesian Optimization Based Grid Point Allocation for LPV and Robust Control

Abstract

This paper investigates systematic selection of optimal grid points for grid-based Linear Parameter-Varying (LPV) and robust controller synthesis. In both settings, the objective is to identify a set of local models such that the controller synthesized for these local models will satisfy global stability and performance requirements for the entire system. Here, local models correspond to evaluations of the LPV or uncertain plant at fixed values of the scheduling signal or realizations of the uncertainty set, respectively. Then, Bayesian optimization is employed to discover the most informative points that govern the closed-loop performance of the designed LPV or robust controller for the complete system until no significant further performance increase or a user specified limit is reached. Furthermore, when local model evaluations are computationally demanding or difficult to obtain, the proposed method is capable to minimize the number of evaluations and adjust the overall computational cost to the available budget. Lastly, the capabilities of the proposed method in automatically obtaining a sufficiently informative grid set are demonstrated on three case-studies: a robust controller design for an unbalanced disk, a multi-objective robust attitude controller design for a satellite with uncertain parameters and two flexible rotating solar arrays, and an LPV controller design for a robotic arm.