Sufficient Conditions and Sensitivity Analysis for Optimal Bang-Bang Control Problems with State Constraints

Bang-bang control problems subject to a state inequality constraint are considered. It is shown that the control problem induces an optimization problem, where the optimization vector assembles the switching and junction times for bangbang and boundary arcs. Second order sufficient conditions (SSC) for the stateconstrained control problem are given which require that SSC for the induced optimization problem are satisfied and a generalized strict bang-bang property holds at switching and junction times. This type of SSC ensures solution differentiability of optimal solutions under parameter perturbations and allows to compute parametric sensitivity derivatives. A numerical algorithm is presented that simultaneously determines a solution candidate, performs the second-order test and computes parametric sensitivity derivatives. We illustrate the algorithm with two state-constrained optimal control problems in biomedicine.