The output regulation problem: classical results and new trends

In this talk, we will review the problem of tracking a reference signal, while maintaining closed-loop stability, even in the presence of disturbances, both signals, the reference and disturbances generated by an exogenous system, called the exosystem. We will formulate the classical state-feedback/output feedback regulation problem for linear systems, and then recall the conditions for the solvability of both problems. The case of robust regulation in the presence of parameter variations will also be reviewed, and the results will be stated in terms of the so-called immersion dynamics. Also, the nonlinear regulation systems will be then presented, and a review of some important results both for continuous and discrete systems will be given.
To conclude, we will present new trends in the problem, and give a few open problems in the matter.