Predictive relay control in constrained minimum-time delivery of therapeutic dose

Summary form only given. In this paper, the therapeutic dose delivery problem is formally stated as the problem of controlling nonlinear integrators with saturation constraints on actuation and the state constraints to prevent damage to the normal tissue. We analyze and discuss unique features of the dose control problem, and establish the necessary condition for the time optimality of the control for nonlinear integrating systems is also derived. The result states that the time-optimal policy is achieved when the controller operates at the actuation or the state constraints. The availability of the general optimality result allows us to eliminate the need for solving the optimization program in real time. The role of the predictive controller in the proposed approach is to calculate control inputs leading to the treatment progression at one of the imposed constraints. The feedback of the predictive controller is used to update the predictive model. The main dose controller is the switching controller, which selects the actuation corresponding to the boundary of the allowable set in the space of states and inputs.