Adaptive control of systems described by nonlinear functional differential equations

For a class of uncertain systems, described by controlled nonlinear functional differential equations, an adaptive feedback strategy is presented which guarantees that, for every system of the class and for every admissible reference signal r(·), the system output y(·) asymptotically tracks r(·), in the sense that the error y(t)-r(t)→0 as t→∞, whilst maintaining boundedness of the adapting parameter. Admissible reference signals are bounded absolutely continuous functions with essentially bounded derivative. The controller uses a discontinuous feedback and an adaptive gain function of Nussbaum type. The analysis is performed using set-valued maps, differential inclusions and an application of Barbalat´s Lemma