Data‐driven safe gain‐scheduling control

Abstract

Data‐based safe gain‐scheduling controllers are presented for discrete‐time linear parameter‐varying systems (LPV) with polytopic models. First, ‐contractivity conditions are provided under which the safety and stability of the LPV systems are unified through Minkowski functions of the safe sets. Then, a data‐based representation of the closed‐loop LPV system is provided, which requires less restrictive data richness conditions than identifying the system dynamics. This sample‐efficient closed‐loop data‐based representation is leveraged to design data‐driven gain‐scheduling controllers that guarantee ‐contractivity and, thus, invariance of the safe sets. It is also shown that the problem of designing a data‐driven gain‐scheduling controller for a polyhedral (ellipsoidal) safe set amounts to a linear program (a semi‐definite program). The motivation behind direct learning of a safe controller is that identifying an LPV system requires satisfying the persistence of the excitation (PE) condition. It is shown in this paper, however, that directly learning a safe controller and bypassing the system identification can be achieved without satisfying the PE condition. This data‐richness reduction is of vital importance, especially for LPV systems that are open‐loop unstable, and collecting rich samples to satisfy the PE condition can jeopardize their safety. A simulation example is provided to show the effectiveness of the presented approach.