The use of D-robust identification methods in the development of a quasioptimal control (Q1386953)

The synthesis of a physical control object demands, in a sense, the construction of its model. The ordinary situation here is the definition of a class of mathematical objects usually differential, difference, and other equations and the isolation of some parametric subset such that each element of it can be a model of a physical object under study. Also a decision rule is defined, usually as a criterion, which allows to establish the adequacy of some element in the model set to the given object. Applying the probability concept of observations, let us assume that the decision rule is single-valued (at least asymptotically) for almost all possible data arrays generated by exact observations. A model adequate in the sense of this rule will be called true. The uncertainty of knowledge of model parameters is, of course, no unsurmountable obstacle in control development. The currently popular method in control theory, namely robust control, proposes a wide class of solutions in the framework of quasioptimal control for a family of models. However, the wider the family is, the more difficult it is to realize the control with satisfactory properties. The author of the paper considers the influence of measurement errors on the exactness of the model identification of physical objects, and thus on the efficiency of their control. The class of D-robust estimations is introduced, for which the bias has an upper bound proportional to the intensity of the distorsions. The value of the proportionality coefficient defines the maximum possible bias and can be defined in advance in the design or in the choice of an algorithm. The last section of the paper contains a technical example concerning the development of adjustment algorithms for the Adaptive Antenna Lattice (AAL) stable with respect to sensitive element failures and to errors in the support signal formation. The aim of the AAL application is to decrease the signal/noise ratio (SNR) at the antenna output (here noise is the input noise). The task of the AAL is to recognize and eliminate the noise. The author proposes a recurrent adjustment algorithm for the processing of AAL signals. The algorithm efficiency was checked by the Monte Carlo method of independent tests for conditions proposed by the client. The test illustrates complete agreement with the theoretical results.