Dynamical Reconstruction of Inputs for Contraction Semigroup Systems: Boundary Input Case

Regularized Extremal Shift in Problems of Stable Control

“…No additional information on the functions v(·) and u(·) is required. We construct a corresponding modification of the method of extremal shift, using, according to [4][5][6][7][8][9], the idea of its local regularization. Along with measuring the phase states at discrete time moments (see (4)), we also consider the case of "continuous" measuring of the states x(t) and w(t).…”

A deconvolution problem related to a singular system

“…The case B 2 = {0} corresponds to a regular system. This case has been studied, for example, in [12,13]. The case B 1 = {0} boils down to solve the problem…”

“…The computation of the pseudoinverse has been thoroughly investigated and it is by now well understood [10]. Hence, we shall assume B 1 = {0} so that the problem that we are studying is an intermediate case, between the computation of the pseudoinverse of an operator and the deconvolution problem as studied in [12,13]. We note however that the proof in [13] uses the assumption that the operator A generates a cosine operator while the proof in [12] assumes that the semigroup e At is contractive.…”

“…Hence, we shall assume B 1 = {0} so that the problem that we are studying is an intermediate case, between the computation of the pseudoinverse of an operator and the deconvolution problem as studied in [12,13]. We note however that the proof in [13] uses the assumption that the operator A generates a cosine operator while the proof in [12] assumes that the semigroup e At is contractive. In this paper cosine operators are not used and, moreover, the techniques of the present paper can be used to remove the contractivity assumption.…”

“…It has been already used both for finite dimensional systems (see, for example, [5,11]) and for classes of distributed systems, see, for example, [12,13].…”