We propose an Aristotle’s mechanics based method for synthesis of analytic control strategies for a flock of unmanned mobile robots. Synthesized strategies ensure bypass prohibited areas, non-collision of elements in the flock, preservation of the flock integrity, and fulfillment of the common goal.

In spite of the system identification, as (in accordance to L. Ljung (2010)) a science and art of constructing mathematical models via sample data, is a polyhedral process, selecting an identification criterion within an identification problem statement is a constituent part requiring both accounting its adequacy to the data available and practical suitability of implementation. The paper presents an approach to the identification of input/output mappings of stochastic systems in accordance to information-theoretic criteria that are derived by constructing a symmetric divergence measure based on Tsallis entropy of an arbitrary order. Meanwhile, a parameterized description of the system under study is utilized combined with a corresponding technique of estimation of the mutual information constructed by use of Tsallis entropy. This leads, finally, to a problem of the finite dimensional optimization to be solved by a suitable technique.

In this paper we study differential invariants and give a local classification of the second order linear differential operators, acting in sections of line bundles, and a local classification of corresponding differential equations.

Statistical linearization is just a kind of stochastic system identification problems, which are considerably influenced with measures of dependence of random values. Within the context, selecting a consistent measure of dependence as a main instrumental tool plays a decisive role. In the present paper, the derivations are based on constructing (symmetric) Tsallis relative entropy (relative entropy is also commonly referred as mutual information) as a basis to formulate the corresponding information-theoretic criterion of the statistical linearization of a system described by an input/output mapping and driven with Gaussian white-noise process. As a result, a constructive procedure to derive weight function coefficients of the linearized model is obtained. Simultaneously the problem of the initial non-linear system identifiabilty is solved in the sense that vanishing all these coefficients is equivalent to the stochastic independence of the system input and output processes, what, in turn, means that the system is not identifiable.

Involved in system identification problems, information theory becomes a powerful tool of constructing solutions, in first turn, as a basis of the final mathematical formalization of identification criteria. Such an orientation unavoidably results in applying corresponding measures of dependence of random values, first of all, based on the mutual information. Meanwhile, this does not mean limiting to the consideration of Shannon approaches only, regarding, correspondingly, Shannon entropy. The present paper proposes applying (symmetric) Tsallis mutual information as a basis to construct an information-theoretic criterion within an input/output system identification problem. Being a consistent, in the sense of the terminology of A.N. Kolmogorov, measure of dependence of random values (a measure that vanishes if and only if the random values are stochastically independent) representing the system and model output variables, the corresponding identification criterion permits, from one hand side, to account the system identifiablity, from another hand side, enables applying fast and efficient computations to solve the problem providing a wide range of applications.