We consider the safe control problem of designing a robustly invariant set using only a finite set of data collected from an unknown input-affine polynomial system in continuous time. We consider input/state/state derivative data that are noisy, i.e., are corrupted by an unknown-but-bounded disturbance. We derive a data-dependent sum-of-squares program that enforces robust invariance of a set and also optimizes the size of that set while keeping it within a set of user-defined safety constraints; the solution of this program, obtained by alternation of the decision variables, directly provides a polynomial robustly invariant set and a state-feedback controller. We numerically test the design on a system of two platooning vehicles.
Data-driven design of safe control for polynomial systems / Alessandro Luppi; Andrea Bisoffi; Claudio De Persis; Pietro Tesi. - In: EUROPEAN JOURNAL OF CONTROL. - ISSN 0947-3580. - STAMPA. - (2023), pp. 1-10. [10.1016/j.ejcon.2023.100914]
Data-driven design of safe control for polynomial systems
Pietro Tesi
2023
Abstract
We consider the safe control problem of designing a robustly invariant set using only a finite set of data collected from an unknown input-affine polynomial system in continuous time. We consider input/state/state derivative data that are noisy, i.e., are corrupted by an unknown-but-bounded disturbance. We derive a data-dependent sum-of-squares program that enforces robust invariance of a set and also optimizes the size of that set while keeping it within a set of user-defined safety constraints; the solution of this program, obtained by alternation of the decision variables, directly provides a polynomial robustly invariant set and a state-feedback controller. We numerically test the design on a system of two platooning vehicles.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.