In the article, based on the estimate of the Euclidean norm of the deviation of the coordinates of the transition and stationary states of the dynamic system, the compression condition of the generalized projection operator of the dynamic system with restrictions is derived. From the principle of contracting mappings, taking into account the derived compression condition of the projection operator, estimates are obtained for the sufficient condition for the stability of the dynamic system of stabilization of the equilibrium position and program motions. The obtained estimates generalize the previously obtained results. Ensuring the stability of the operator of a limited dynamic system is demonstrated experimentally.

Keywords: sufficient condition for stability, projection operator, stabilization of equilibrium position. stabilization of program motions, SimInTech

A complex dynamic system is defined by a structurally invariant operator. The operator structure allows formulating problems of stabilizing program motions or equilibrium positions of a complex dynamic system with constraints on state coordinates and control. The solution of these problems allows synthesizing a structurally invariant operator of a complex dynamic system with inequality-constraints on the vector of locally admissible controls and state coordinates. Computational experiments confirming the correctness of the synthesized structurally invariant projection operator are performed.

Keywords: structurally-invariant operator, stabilization of program motions, complex nonlinear dynamic system, projection operator, SimInTech

The paper presents the formulation of problems of minimization and maximization of a linear functional with inequality constraints on the vector of admissible program motions and equality constraints specified by a linear manifold. An analytical solution is synthesized that determines the projection operator for solving the specified mathematical programming problems with equality constraints and inequalities. An analytical solution is obtained that determines the boundary values ​​of the Lagrange multiplier for the synthesized projection operator. The correctness of the obtained solution is illustrated.

Keywords: mathematical programming, linear functional, projection operators, admissible program motions, stabilization of program motions, SimInTech