Sufficient conditions and sensitivity analysis for optimal bangbang control problems with state constraints

Abstract Bang–bang control problems subject to a state inequality con-straint are considered. It is shown that the control problem induces an op-timization problem, where the optimization vector assembles the switching and junction times for bang–bang and boundary arcs. Second order suffi-cient conditions (SSC) for the state–constrained 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 junc-tion 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 simultane-ously 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