Applications
Optimal control of bacterial chemotaxis system
The following example comes from p. 20-21 of Pearson.[3] Chemotaxis is the movement of an organism in response to an external chemical stimulus. One problem of particular interest is in managing the spatial dynamics of bacteria that are subject to chemotaxis to achieve some desired result. For a cell density and concentration density of a chemoattractant, it is possible to formulate a boundary control problem:
where is the ideal cell density, is the ideal concentration density, and is the control variable. This objective function is subject to the dynamics: where is the Laplace operator.