A Nonlinear Optimal Control Approach for Bacterial Infections Under Antibiotics Resistance

The overuse and misuse of antibiotics has become a major problem for public health. People become resistant to antibiotics and because of this the anticipated therapeutic effect is never reached. In-hospital infections are often aggravated and large amounts of money are spent for treating complications in the patients’ condition. In this paper a nonlinear optimal (H-infinity) control method is developed for the dynamic model of bacterial infections exhibiting resistance to antibiotics. First, differential flatness properties are proven for the associated state-space model. Next, the state-space description undergoes approximate linearization with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. The linearization process takes place at each sampling instance around a time-varying operating point which is defined by the present value of the system’s state vector and by the last sampled value of the control inputs vector. For the approximately linearized model of the system a stabilizing H-infinity feedback controller is designed. To compute the controller’s gains an algebraic Riccati equation has to be repetitively solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. The proposed method achieves stabilization and remedy for the bacterial infection under moderate use of antibiotics.