Vol 77, No 1 (2016)

Consideration was given to the problem of robust stochastic filtering in a finite horizon for the linear discrete time-varying system. A random disturbance with inaccurately known probabilistic distribution is fed to the system input. Uncertainty of the input disturbance is defined in the information-theoretical terms by the anisotropy functional of a random vector. The sufficient condition for strict boundedness of the anisotropic norm of linear discrete timevarying system assigned by the threshold value (lemma of real boundedness) was proved in terms of the matrix inequalities. Sufficient conditions for boundedness of the anisotropic norm of two limiting cases of the anisotropy levels of the input disturbance (a = 0 and a → ∞) were established. A sufficient existence condition for the estimator guaranteeing boundedness of the anisotropic norm of the estimation error operator by the given threshold value was formulated and proved. Sufficient existence conditions for the estimators of two limiting cases of the anisotropy levels of input disturbance were obtained. The estimation algorithm relies on the recurrent solution of a system of matrix inequalities.

This paper is concerned with the probability-constrained filtering problem for a class of time-varying nonlinear stochastic systems with estimation error variance constraint. The stochastic nonlinearity considered is quite general that is capable of describing several well-studied stochastic nonlinear systems. The second-order statistics of the noise sequence are unknown but belong to certain known convex set. The purpose of this paper is to design a filter guaranteeing a minimized upper-bound on the estimation error variance. The existence condition for the desired filter is established, in terms of the feasibility of a set of difference Riccati-like equations, which can be solved forward in time. Then, under the probability constraints, a minimax estimation problem is proposed for determining the suboptimal filter structure that minimizes the worst-case performance on the estimation error variance with respect to the uncertain second-order statistics. Finally, a numerical example is presented to show the effectiveness and applicability of the proposed method.

This paper derives recurrent expressions for the maximum attainable estimation accuracy calculated using the Cramér–Rao inequality (Cramér–Rao lower bound) in the discretetime nonlinear filtering problem under conditions when generating noises in the state vector and measurement error equations depend on estimated parameters and the state vector incorporates a constant subvector. We establish a connection to similar expressions in the case of no such dependence. An example illustrates application of the obtained algorithms to lowerbound accuracy calculation in a parameter estimation problem often arising in navigation data processing within a model described by the sum of a Wiener sequence and discrete-time white noise of an unknown variance.

Representing the basic concept of this paper, cognitive map is used to construct a cognitive linear dynamic model with a bounded state space. We consider the problem of transferring this model from an arbitrary initial state to some asymptotically stable state belonging to a neighborhood of a given state. We suggest two classes of controls and introduce the transfer “quality” as the proximity of the resulting steady state to the desired state. And finally, an illustrative example is provided.

We suggest a routine for automatic estimation of complexity and difficulty of educational tasks. This routine is based on syntactic text analysis, phrases’ predicative structures identification, and semantic network construction. Then we develop a mathematical model which employs a notion on semantic distance between notions–words to calculate the amount of knowledge in a semantic network. We show that the amount of knowledge in a semantic network is a measure in the set of all semantic networks, and the semantic distance makes this set the metric one.