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Inverse optimal control for positive impulsive systems toward personalized therapeutic regimens

Infectious diseases are latent threats to humankind. Control theoretical approaches can help practitioners to advance the scheduling of drugs. For the case of infectious diseases, it is not possible to keep continuous flow of drug administration over all time‐steps, thus the action of the control input has to be restricted at some of the kth instants. This paper presents the adaptation of inverse optimal control to positive impulsive systems in discrete‐time to schedule therapies. The properties of positive systems are used to simplify the control design. Thus, the problem of scheduling therapies in infectious diseases is illustrated with influenza and COVID‐19. Numerical results show the applicability of the control algorithms.