Some notes on output regulation of nonlinear systems

Known schemes for output regulation implies the existence of suitable controlled invariant sets, i.e. sets union of trajectories solution of the exact tracking problem. For linear systems and for a particular class of nonlinear systems, these invariant sets are sought as the solution to a set of algebraic and partial differential equations. More generally, invariant sets for output regulation can be characterized as the search for “acceptable” solutions to the exact tracking problem, i.e. solutions satisfying some constraint like internal stability. After a review of the search for these invariant sets in known schemes for output regulation, the author discusses the possibility of using inversion techniques even in the case of nonminimum phase systems. A procedure based on a known iterative technique is presented for systems with quasilinear internal dynamics. Some academic examples illustrate the ideas introduced