Optimal Control Effect into Innate Immune System

Monocytes (M) and macrophages (Mφ) cells are mononuclear essential components of the innate immune system response. (M) and (Mφ) are mononuclear phagocytes that have crucial distinct roles in tissue homeostasis and immunity. (M) are key players during inflammation and pathogen challenge also are precursor of (Mφ), whereas tissue resident (Mφ) have important functions in development, tissue homeostasis and the resolution of inflammation. They comprise what was just recently recognized as a heterogeneous family of professional phagocytic cells responsible for the recognition and clearance of pathogens and dead cells. Optimal Control equations for the state x
₁
(t) with tracking in the state x
₂
(t) has been applied to two dimensional system of differential not homogeneous equations presented in [15], [7]. This system represents the behavior of (M) and (Mφ) into the blood flow. Special form of matrices H and Q in the cost criterion function J is given for obtain the convergence of the state variables ((M) and (Mφ)) to optimal asymptotic values (health state) when the production rate λ is modified.