Optimal Impulsive Control With Application to Antiangiogenic Tumor Therapy

An optimal control algorithm is proposed for impulsive differential systems, i.e., systems evolving according to ordinary differential equations between any two control actions, occurring impulsively at discrete-time instants. Measurements are as well acquired at discrete-time instants. A model-based control law is conceived for medical and healthcare frameworks and, indeed, is applied to synthesize a feedback antiangiogenic tumor therapy. To cope with unavailable or temporally sparse measurements, the control law benefits a state observer properly designed for continuous-discrete systems by suitably exploiting recent results on observers for time-delay systems. The closed-loop algorithm is validated by building up an exhaustive simulation campaign on a population of virtual subjects, each sampled from a multivariate Gaussian distribution whose mean and covariance matrix is identified from experimental data taken from the literature. In silico results are encouraging and pave the way to further clinical verifications.