Bilinear Social and Biological Control Systems

Finite state bilinear systems are described by a system of differential equations which are linear in state, linear in control, but not jointly linear in both as are traditional linear systems. An introduction to the physical relevance of these systems, their controllability and optimal control is analyzed in references [i] and [2]. It is shown that linear system controllability and performance may be improved by the addition of a bilinear control mode. This is as it would be expected since the bilinear system does exhibit a form of adaptive control and variable structure. These are the reasons that bilinear systems, or at least their approximation, are so common in natural and societal processes as well as in engineering.