Controlled functional differential equations and adaptive tracking

Adaptive tracking control of a class N of single-input, single-output systems described by nonlinear functional differential equations is considered: the control objective is that of tracking, by the system output, of reference signals of class R (absolutely continuous and bounded with essentially bounded derivative). A (N,R) -universal servomechanism, in the form of an adaptive error feedback strategy incorporating gains of Nussbaum type, is developed which, for every system of class N and every reference signal of class R, ensures either (i) practical tracking (in the sense that prespecified asymptotic tracking accuracy, quantified by λ>0, is assured), or (ii) asymptotic tracking (in the sense that the tracking error approaches zero). The first case (i) is achievable by continuous feedback; the second case (ii) necessitates discontinuous feedback. Both cases are developed within a framework of functional differential inclusions.