Direct Data‐Driven State‐Feedback Control of Linear Parameter‐Varying Systems

ABSTRACT The framework of linear parameter‐varying (LPV) systems has shown to be a powerful tool for the design of controllers for complex nonlinear systems using linear tools. In this work, we derive novel methods that allow us to synthesize LPV state‐feedback controllers directly from only a single sequence of data and guarantee stability and performance of the closed‐loop system. We show that if the measured open‐loop data from the system satisfies a persistency of excitation condition, then the full open‐loop and closed‐loop input‐scheduling‐state behavior can be represented using only the data. With this representation, we formulate data‐driven analysis and synthesis problems, where the latter yields controllers that guarantee stability and performance in terms of infinite horizon quadratic cost, generalization of the ‐norm, and ‐gain of the closed‐loop system. The controllers are synthesized by solving a semi‐definite program. Additionally, we provide a synthesis method to handle noisy measurement data. Competitive performance of the proposed data‐driven synthesis methods is demonstrated w.r.t. model‐based synthesis in multiple simulation studies, including a nonlinear unbalanced disc system.