Biological Modeling Project

Description: Animal and human development and growth is a very complex process.  The full size of an animal is mostly specified by its genes with some influence due to perturbations by its environment.  An animal starts out as a single cell and ends up at full size with perhaps a trillion or more cells.  The animal also has two "stopping" criteria.  When it reaches its target size it stops growing but if it was perturbed during growth by say malnutrition or disease it will still stop growing after a fixed point in time even if it did not reach its full potential.  Growth is extremely complex but at its most basic level growth takes place when growth hormone is present and stops when it is no longer present (reality is much more complicated of course but this is a good zeroth order assumption).   Growth is also a purely local process.  The cells only know what is going on in their immediate environment and through a global signal that is transmitted by the hormones through the body's circulation system.  Finally, all the biochemical processes in the body have short time constants compared to the growth cycle. The slowest (linear) time constants may be on the order of days perhaps but growth takes place on the order of years and for humans decades.

Project goals: Design a control system for self-directed growth that only uses local information.  The system must start extremely small and grow 10 or more orders of magnitude to some prescribed target and then stop.  However, it cannot "externally" measure it self to know if it has reached its target.  It must somehow keep track using only local information.  The tolerance must also be quite precise.  If unperturbed, it needs to reach its target size within a small error tolerance, say 5%.  The system must be robust in the presence of stochastic forcing.  To make this project interesting, the growing body must have a spatial extent and each location of space can only access local information and some growth substances that can diffuse quickly across the medium.  The system is allowed to have feedback from the environment but this is limited only things that can be measured locally by each spatial point.  Finally, the system is only allowed to have short fixed time constants with respect to the length of time of growth.  For instance, you cannot simply put in a very slowly decaying variable that stops when it hits a threshold.  It's okay to have a slow trajectory built in but it has to be in a system where the linear time constants are short.  So the slow time could be due to being close to a homoclinic orbit for example.