Preliminary results about robust lagrange stability in adaptive non‐linear regulation

We are concerned with the problem of regulating the equilibrium point of a non‐linear system in the presence of both parametric and dynamic uncertainties. For the parametric uncertainty we propose a new adaptive controller based on a Lyapunov design and guaranteeing the global boundedness of the solution if a growth condition is satisfied. For the dynamic uncertainty we propose a new way of characterizing the unmodelled effects which encompasses some singular and regular perturbations as illustrated by our worked example. Finally we show how, by modifying the above controller, the boundedness property can be made robust to these unmodelled effects.