ASYMPTOTIC OBSERVERS FOR A CLASS OF EVOLUTION-EQUATIONS - A NONLINEARAPPROACH

We consider in a Hilbert space H the system (E-u) = {(x) over dot = uA x+B(x); y = [x, c](H)}, where the control u is an element of L-infinit y([0,+infinity[,R+) multiplies a possibly unbounded m-dissipative line ar operator A. The operator B is nonlinear dissipative, and y stands f or the output of the system. We prove, in this nonlinear framework, th e existence of a suitable Luenberger-like observer. For this purpose, we show that the usual notions of regularly persistent inputs proposed in [7] or [4] are the appropriate concepts that allow one to generali ze the main results of [9] and [8] or [7] for bilinear systems to our nonlinear general system: For each regularly persistent input, the est imation error of the observer converges weakly to zero. If in addition A generates a compact semigroup, the estimation error converges stron gly to zero. A prototype of such a system is the heat exchanger system described in [9] or [8].