Parameter Uncertainty in State Constrained Optimal Control Problems
Fernando Pereira, Dmitry Karamzin, Valeriano Oliveira, Geraldo Silva
This work considers state constrained optimal control problems in the presence of parameter uncertainties and provides necessary conditions in the form of a maximum principle. The uncertain parameter is represented by a vector taking values in a given compact set in a metric space and that might affect both the objective function and the dynamics. The necessary conditions obtained here are a generalization of the mini-max maximum principle derived earlier for optimal control problems in that, now, we consider state constraints. Moreover, our set of necessary conditions is different from the fact that they are formulated in the Gamkrelidze framework.