On-line reconstruction of inputs to a class of distributed parameter systems

keywords Input reconstruction, deconvolution, holomorphic semigroups Reconstruction of input signals to linear dynamical systems is an important problem. In fact, in the time invariant case, it is a special instance of the deconvolution problem. Several algorithms have been proposed to achieve this goal, which can be classified in two large classes: off-line and on-line deconvolution algorithms. Off-line deconvolution algorithms accumulate all the available pieces of information and, after the process has come to an end, these pieces of information are elaborated so to obtain an estimate of the input signal. An example of this is Tikonov method. On-line deconvolution methods instead at the time t produce an estimate v(t) of the unknown input u at the time t solely on the basis of observations taken at previous times. Of course, solely the algorithms in this class can be used for regulation and control purposes, see applications in [2, 3] for the case of finite dimensional systems. In this talk we present an extension of the algorithm proposed in [1] (a paper concerned with finite dimensional systems) to the on-line identification of inputs to a class of distributed systems. The class of systems we consider in this talk is described in the time domain