Innate Immune Response via Perturbed LQ - Control Problem

In this paper we consider a perturbed linear-quadratic control problem on a finite interval. The only difference from the traditional LQ-control problem is that the problem has an extra linear term in the cost function which makes it time-dependent. The major motivation for this extension comes from [4] where we consider applications of very efficient primal-dual interior-point algorithms to the computational analysis of multi-criteria linear-quadratic control problems in minimax form. It turns out that the linear-quadratic control problem on a finite interval with the linear term in the objective function can also be applied in the optimal control of innate immune response which is considered in [5].