Time-varying and adaptive integral control of infinite-dimensional regularlinear systems with input nonlinearities

Closing the loop around an exponentially stable, single-input, single-outpu t, regular linear system subject to a globally Lipschitz, nondecreasing act uator nonlinearity and compensated by an integral controller with time-depe ndent gain k(t) is shown to ensure asymptotic tracking of a constant refere nce signal r, provided that (a) the steady-state gain of the linear part of the system is positive, (b) the reference value r is feasible in an entire ly natural sense, and (c) the function t--> k (t) monotonically decreases t o zero at a sufficiently slow rate. This result forms the basis of a simple adaptive control strategy that ensures asymptotic tracking under condition s (a) and (b).