Inversion-based output regulation of chemotaxis using a constrained influx of chemical signaling molecules

This paper considers the output regulation of the delivery of chemical signaling molecules to control the movement of cells that act in response to chemical gradients in a phenomenon known as chemotaxis. This study is motivated by recent efforts by tissue engineers to employ chemotaxis to coax cells into developing or regenerating biological tissues and organs. The control problem is to determine the time-varying spatial positioning of and mass flow rate through the tip of a needle that squirts chemical signaling molecules into a fluid where the cells live. The approach is mathematically formulated and the constrained output regulation problem of coupled partial differential equations is solved by combining an inversion-based approach with a finite-volume method in the temporal domain and receding-horizon control. The on-line computational cost is sufficiently low for this control technology to be employed in an experimental system.