Nonlinear optimal control for the multi-variable tumor-growth dynamics.

The multivariable tumor-growth dynamic model has been widely used to describe the inhibition of tumor-cells proliferation under the simultaneous infusion of multiple chemotherapeutic drugs. In this article, a nonlinear optimal (H-infinity) control method is developed for the multi-variable tumor-growth model. First, differential flatness properties are proven for the associated state-space description. 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 instant 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. Finally, the performance of the nonlinear optimal control method is compared against a flatness-based control approach.