Data-driven nonlinear output regulation via data-enforced incremental passivity

This work proposes a data-driven nonlinear regulator design that achieves asymptotic reference tracking under external disturbances, where the reference and disturbances are generated by a linear exosystem. The key idea is to design a data-driven feedback controller such that the closed-loop system is incrementally passive with respect to the regulation error and a virtual input. By interconnecting the closed-loop system with an internal model and carefully designing the virtual input, we solve the data-driven nonlinear output regulation problem. We characterize the passivation feedback controller by a set of data-dependent linear matrix inequalities, which is independent of the internal model. This decoupled design offers high data efficiency and design flexibility. The proposed approach also solves the non-zero equilibrium stabilization problem of a class of nonlinear systems with unknown equilibrium input. Numerical examples are presented to illustrate the effectiveness of the proposed designs.