Feedback Optimal Control Problem for a Network Model of Viscous Fluid Flows
Evgenii S. Baranovskii
Abstract
We study a feedback optimal control problem for a three-dimensional model of a stationary flow of a non-Newtonian fluid (with variable viscosity) in a pipeline network with complex geometry. The control parameter is the dynamic pressure on connection surfaces of pipes to nodes. The flow model is a mixed boundary-value problem for a system of strongly nonlinear partial differential equations in a netlike domain with Kirchhoff-type transmission conditions at interior nodes of the network. The solvability of the optimization problem in the weak formulation is proved; namely, we establish sufficient conditions for the existence of a weak solution which minimizes a lower semicontinuous cost functional.
Topics & Concepts
MathematicsViscosityBoundary value problemNonlinear systemFlow (mathematics)Domain (mathematical analysis)Connection (principal bundle)Partial differential equationViscosity solutionControl theory (sociology)Mathematical analysisOptimal controlMathematical optimizationApplied mathematicsControl (management)GeometryComputer sciencePhysicsQuantum mechanicsArtificial intelligenceAdvanced Mathematical Modeling in EngineeringStability and Controllability of Differential EquationsDifferential Equations and Numerical Methods