Optimal control of the linearized Navier— Stokes system in a netlike domain

Abstract

This work is a natural extension of research into optimal control problems of evolution equations with distributed parameters on a geometrical graph (network) of one of the authors in the direction of increasing the dimension of a spatial variable and the functions describing the state of the study of the Navier-Stokes equations. At the same time is examined a simple case of the absence of convective effect (laminar flow of an incompressible viscous fluid)linearized system of Navier-Stokes equations in a net-like domain. It proves unique solvability of the initial boundary value problem in the weak formulation which is based on the Faedo-Galerkin method using a special basis (the set of generalized eigenfunctions of the special spectral problem) and a priori estimates of norms solutions such as power inequalities. The proof is constructive: to construct a sequence of approximate solutions that converges weakly to the exact solution of the problem. Problems are analyzed with distributed and a start control with a final observation, widespread in applications, that provides the necessary and sufficient conditions for the existence of optimal controls in terms of the conjugate states of the respective systems. Sufficient attention is paid to the synthesis of the optimal control action, and analogues of established finite-dimensional case for Kalman results have been obtained. Although, the use of this method is demonstrated by examples of optimal control theory, this method has a highly susceptible to generalization and applicable to a wide class of linear problems. Refs 15.

Stability of weak solutions of parabolic systems with distributed parameters on the graph

“…The approach presented by the statements of theorem 3-5 may be used to obtain conditions of stability (asymptotic stability) of weak solution of initialboundary value problem (4), (5). The same approach applies to both tasks, space variable x which has a dimension of large 1 (x ∈ R n , n 2) and for many-dimensional functions that describe the state of researched system [14][15][16]. The results are fundamental in tasks of optimal control and stabilization of differential systems with time-delay [17][18][19][20][21][22][23][24][25][26][27][28].…”

Method of Calculation of Institutional Investors Stability under Conditions of Digital Economy

“…It is caused by possibility of replication of results and also realization of the received algorithms as a part of expert systems and the automated program complexes for consultation of experts and the help in decision-making. At the stage of formation of conditions for modeling [2] of activity of the institutional investor, it is necessary to consider that such serious players of this segment of business as insurance companies work in the conditions determined by high dispersion of function of distribution of approach in terms of payments to the clients. It results in need to make investments in highly liquid assets.…”

Significance of Double Stratification in Stagnation Point Flow of Third-Grade Fluid towards a Radiative Stretching Cylinder

“…In present study the analysis is carried out by finding the optimal convergence. For details one can read the optimal control convergence procedure adopted in solving linearized Navier-Stokes equations in netlike domain [23] and pipeline flow [24].…”