2 - Some General Optimal Control Problems Useful for Biokinetics

Abstract

The problem of optimal control is also related to that part of purely variational problem, when the kinetic term depends not only on the derivatives but also on the variables themselves. So the phase space of state variables is not homogeneous in the sense of dissipative mechanisms as it is in mechanics. On the basis of the examples of application of the variational/ optimal control method considered in the chapter, some conclusions are drawn. Both in the case of one- and multidimensional kinetics, the control can be introduced into the known biological models by means of the rate changes or the rate constants in dynamic systems reflecting some mechanisms. In fact, it is a formulation of the extreme approach employing the combination of variational calculus and the optimal control; and it is also a possible way to extend the ideology of the least action principle into biology. The application of the Lagrangian in the form of a sum of only positively defined terms results in the difficulty in a non-contradicting interpretation of the first integral, which is interpreted as energy in physics. The introduction of the optimal control to linear kinetics in the multiplicative form can result in complex model of regulation.