On July 5, 2026, Academician of the Russian Academy of Sciences, Doctor of Physical and Mathematical Sciences Stanislav Nikolaevich Vassilyev celebrates his 80th birthday. The jubilarian is an outstanding scientist, a specialist in the fields of mathematical cybernetics, systems analysis, control theory, and artificial intelligence. His scientific developments, which combine fundamental mathematics with applied problems of dynamics analysis and intellectualization of control of complex systems, have gained recognition both in Russia and far beyond its borders.

A method is proposed for finding reachable values of the output vector, taking into account constraints on the input and output signals during the control process for linear discrete systems with variable parameters. The developed algorithm overcomes the computational limitations of traditional approaches when working with high-order models. The method is based on sequential analysis of the output vector components by reducing them to linear programming problems. Its application is demonstrated using the example of the Globus-M2 spherical tokamak plasma model, where the possibility of determining attainable plasma configurations under constraints on the control voltages and currents is shown.

The problem of parametrization of suboptimal and γ-optimal anisotropic controllers in the form of static state feedback for linear discrete-time invariant systems driven by stochastic disturbances with bounded mean anisotropy is considered. In the controller design problem, the solution is based on applying Finsler lemma to the system of inequalities characterizing the boundedness of the anisotropic norm by some number. The relation of the solution of this problem to the solution of the controller design problem for suboptimal and γ-optimal anisotropic controllers via convex optimization without parametrization is pointed out. An example demonstrating the efficiency of the proposed approach to parametrization of anisotropic controllers is provided.

This paper considers the problem of transforming a fuzzy signal by a linear dynamic system described by a linear differential equation of high order with variable real coefficients, a fuzzy-valued inhomogeneity, and fuzzy initial conditions. By assumption, certain numerical average characteristics of the fuzzy-valued input signal (fuzzy means and fuzzy half-ranges) are known. Based on these characteristics and system parameters, the corresponding numerical average characteristics of the fuzzy signal at the output are established. Methods of fuzzy mathematics and the theory of ordinary differential equations are used. As an application, the model of a series resonant radio circuit with a fuzzy-valued input signal is considered.

This paper considers time-varying linear and nonlinear systems of differentialalgebraic equations with a scalar observable output. In the linear case, sufficient detectability conditions are established, and a state observer is designed. For systems with a controlled input of a special form, a stabilization procedure using dynamic output feedback is proposed. Based on a linear approximation, detectability conditions are derived for a nonlinear system.

This paper considers the problem of constructing reachable domains for a planar two-link manipulator with a statically balanced second link under time-optimal control of its motion with angular velocity constraints for the links. The optimal controls belong to the class of relay regimes and contain the minimum total number of switchings sufficient to satisfy the boundary conditions: the system is at rest at the initial and final time instants. A method is developed to find reachable domains in the manipulator’s configuration plane under the proposed controls with angular velocity constraints.

A rigid body under the action of a linear dissipative torque and an essentially nonlinear restoring one is considered. It is assumed that there is a constant delay in the restoring torque. Using a special construction of the Lyapunov–Krasovsky functional, it is proved that the given orientation of the body is asymptotically stable for any value of delay. In addition, the case is investigated where the body is subject to PID-like controller with linear differential part and essentially nonlinear integral and proportional ones. The admissible values of the controller parameters are determined, for which it solves the problem of triaxial stabilization. The results of numerical modeling are presented, confirming the established theoretical conclusions.

The problems of decision-making are considered when preferences are estimated on an ordinal scale, and the possibilities of realizing the values of an uncertain factor are described by a qualitative probability (complete or only partial). Definitions of preference and indifference relations on a set of strategies are introduced. Simple decision rules are proposed that allow comparing strategies by preference. Examples of their application are given.