Optimal impulsive control with application to antiangiogenic tumor therapy

An optimal control algorithm is proposed for impulsivedifferential systems, i.e. systems evolving according toordinary differential equations between any two control actions,occurring impulsively at discrete time instants. Measurementsare as well acquired at discrete time instants. The model-basedcontrol law is conceived for medical and health-care frameworksand, indeed, is applied to synthesize a feedback antiangiogenictumor therapy. To cope with unavailable or temporally sparsemeasurements, the control law benefits of a state observerproperly designed for continuous-discrete systems by suitablyexploiting recent results on observers for time-delay systems. Theclosed-loop algorithm is validated by building up an exhaustivesimulation campaign on a population of virtual subjects, eachsampled from a multivariate Gaussian distribution whose meanand covariance matrix are identified from experimental datataken from the literature. In silico results are encouraging andpave the way to further clinical verifications.