Nonlinear optimal control for the abatement of viral infections' spreading

The necessity for implementing optimal control against epidemics comes from the scarcity of the resources for treating infectious diseases in terms of vaccines, antiviral drugs and other medical facilities. To achieve a solution for the optimal control problem of the dynamics of viral spreading, the state-space model of the infectious disease undergoes first approximate linearization around a temporary operating point which is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the computation of the associated Jacobian matrices. For the approximately linearized model of the epidemics an optimal (H-infinity) feedback controller is developed. For the computation of the controller's feedback gains an algebraic Riccati equation is solved at each iteration of the control algorithm. Through Lyapunov stability analysis the global asymptotic stability properties of the control scheme are proven.