Enhancing Immune System Response Through Optimal Control.

The aim of this chapter is to introduce you to some ideas about modelling non-linear systems from first principles, about their behaviour and how it can be analyzed, and finally, about how they might be made to behave in a desirable way. As a vehicle I have chosen what I hope you will find to be an interesting problem which is outside the mainstream of technology-based control but is, I believe, part of an area of increasing importance for the near future. The topic is the application of control theory in a biological setting - the optimal enhancement of the immune system. In what follows I will first outline how models of systems of this type can be constructed largely through deduction. They belong to a class of models called Lotka-Volterra Models which are widely used to describe the dynamics of interacting populations such as predator-prey systems, epidemics and, in our case, the concentrations of various biological quantities in the immune system. Next we will look briefly at the behaviour of this class of dynamics. Finally we look at a difficult problem - how control theory can be used to enhance the response of the immune system by allowing us to compute an optimal policy that will prevent organ failure in conditions where, left to itself, organ damage or death would naturally occur. The case study builds on a series of recent papers by Stengel and colleagues [1-3] with the introduction of a newly developed approach to non-linear optimal control [4] which has not yet become well known but appears to have a number of advantages over conventional solutions. Throughout I will try to maintain a "systems viewpoint" and avoid too much biology. I will also avoid too much mathematics other than stating the key equations and providing references to more detail. Those of you versed in linear quadratic optimal control will recognize the form of the non-linear generalization. [ABSTRACT FROM AUTHOR]