NUMERICAL-SOLUTION OF A DRUG DISPLACEMENT PROBLEM WITH BOUNDED STATE VARIABLES

The interaction of the two drugs warfarin and phenylbutazone has previously been considered as a time-optimal control problem with state inequality constraints. We include bounds for the control and show that necessary optimality conditions and junction conditions for bounded state variables lead to boundary value problems with switching and junction conditions. A special version of the multiple-shooting algorithm is employed for solving the different types of boundary value problems. The switching structure of the optimal control is determined for a range of parameters in the state constraint. Owing to the special structure of the control, a state space solution is obtained in a first step which reduces the numerical complexity of the problem. It is shown how the numerical results can be used to compute the generalized gradient of the optimal value function explicitly.