The article is devoted to solving the problem of controlling a system defined by ordinary differential equations with a nonlinear right-hand side, which has the property of quasi-monotonicity with respect to off-diagonal elements. The equations also contain control parameters and uncertainties (errors), the possible values of which should satisfy some point-wise restrictions. The problem of control over a finite time interval is considered in order to transfer the state of the system to a given target set. The current state of the system is unknown, and for the formation of a control strategy, only a priori estimates of the initial state are available, as well as the results of incomplete and inaccurate measurement results received online. To solve the problem, a well-known general scheme is used, according to which it is necessary to consistently solve three subtasks: the approximate construction of information sets of the system, solvability sets, and, finally, the control synthesis problem. In this paper, this general scheme is successfully implemented for the special class of nonlinear systems under consideration. Theorems on external interval estimates of information sets, internal estimates of solvability sets, as well as on sufficient conditions for the solvability of the control problem are proved. Formulas for feedback control are obtained, depending on the so-called generalized position, formed on the basis of available information about the system and measurement results. The possibility of applying the theoretical results obtained to solve specific control problems is confirmed by the model example analyzed in the work.
P. A Tochilin (Wed,) studied this question.