SCIENCE & EDUCATION

 This note deals with a controllability condition for affine systems with scalar control on all space of states for any final interval of time. Research is based on system transformation to a quasicanonical form and the further analysis of terminal problem solution existence for the transformed system. It is shown that for system with the right part of a special form the terminal problem has the solution for any initial and final states of system and any interval of time. Thereby it is proved that such system is controlled on all space of states for any final interval of time. A possible scope of the received results is the solution of technical systems control problems. 

 Control systems that have a linearizing output are called flat. Solutions of such system are expressed through functions of this output and a finite set of their derivatives according to the system. Such output allows to synthesize control algorithm in the form of dynamic feedback. In the article the problem of flatness checking is investigated by methods of infinite-dimensional differential geometry. Earlier this problem was reformulated as the problem of search of an invertible differential operator which transforms a column of given 1-forms to a column of exact 1-forms. In the article an equation for such an operator is derived. The solubility of this equation means flatness of system.

 This note deals with a ship positioning control problem. The dynamics considered are nonlinear ship dynamics on the plane. Only the center of mass coordinates and yaw angle are supposed to be physically measured. The main result states that separation principle holds for the nonlinear model in question. Specifically, the stabilizing control law is synthesized in two steps. First, the state feedback control law is found using the feedback linearization technique. Then, the global asymptotical observer is designed and the observer’s state is put into the state feedback control instead of the system’s state. The resulting system in closed-loop with the observer state feedback is shown to be globally asymptotically stable. The proved theoretical results are also illustrated through simulation.

 A model adequacy test should be carried out on the basis of accurate aprioristic ideas about a class of adequate models, as in solving of practical problems this class is final. This article considers quadratic sums of a dispersive analysis equation and their independence is proved. Necessary and sufficient conditions of existence of adequate models are given. It is shown that the class of adequate models is infinite.