Robust output regulation of nonlinear systems: Semiglobal, global and adaptive

This work focuses on the problem of output regulation for nonlinear dynamical system, namely the one of designing feedback controllers to let the output of a system asymptotically track prescribed trajectories or asymptotically reject unwanted disturbances. The setup we consider is the classical one in which the exogenous signals to be tracked of rejected are generated as trajectories of a linear, time invariant and neutrally stable system. The controller is required to process information from the regulated error only, and has to be designed in spite of parametric uncertainties in the plant model. We address the problem of achieving semiglobal robust regulation (that is, for initial conditions of the plant ranging over arbitrary compact sets) as well as global robust regulation for specific classes of single-input single-output nonlinear systems. Our solution is based on the classical decomposition of the controller into an output-feedback stabilizer and an internal model. It is shown how an adaptive version of our controllers solves the longstanding problem of output regulation in case the frequencies of the exogenous signal are not known a priori.