Optimal control with a bounded number of switchings. I: Formulation of main results. II: Derivation of necessary conditions (Q760655)

The author considers a control problem associated with a differential equation in \(R^ n\), for the case that the number of switchings of some control vector's components is bounded. The first theorem gives conditions for the existence of an optimal control in case of a bounded number of switchings of all control vector's components. In the second theorem, necessary optimality conditions for the control problem under consideration are derived. While in part I no proofs are given, in part II the author proves the second theorem mentioned above. The result is applied to a time-optimal control problem.