A General Optimization Approach

Abstract

Let us now establish an optimization approach for the approximate solution of identification and control problems, but in such a way that the solutions continuously depend upon the input data. In this Chapter 3, we only consider the strictly deterministic and non-Bayesian case (see Sec. 2,3.). The study of the present section deals with the semi-discretization model, i.e., the determination of Banach or Hilbert space elements from an m-dimensional noisy data vector s according to formulae (2.96) and (2.97). In the subsequent Sec. 3.2., we will turn to the full-discretization model, which is concerned with noisy discretized Inverse problems in the sense of Definition 2.63. Furthermore, we have to distinguish the particularities in modelling identification and control problems. For problems arising in case of essentially coupled dimension numbers m and n (see for instance Sec. 2.2.4.), we refer to [209, Sec.3.3.]. Finally, Sec. 3.3. will complete this chapter with a study on the uncertainty of approximate solutions in the identification case.