In this work, we consider an optimal control problem for a generalized model bioconvective flows, which are convection flows caused by the differences in concentration of upward swimming microorganisms fluid. We firstly study existence weak solutions mathematical fluid model; then prove controls and obtain corresponding first order optimality conditions using Dubovitskii-Milyutin formalism.

The optimal visiting problem is the optimization of a trajectory that has to touch or pass as close possible collection target points. does not verify dynamic programming principle, and it needs specific formulation keep track visited In this paper, we introduce hybrid approach by adding discontinuous part switching between group discrete states related targets. Then, show well-posedness Hamilt...