Optimal control problems via a direct method
The paper deals with the minimization problem of a cost functional associated to a nonlinear control process defined in a fixed time interval. The cost functional is of a general form. The paper is organized as follows. First, sufficient conditions are given in order that the considered nonlinear boundary value control problem is solvable by using suitable finite dimensional control spaces. The structure of the relative solution set with respect to these finite dimensional control spaces and its relationship with the solution set corresponding to the entire control space \(L^ r([0,1],R^ m)\) (where \(1\leq r\leq\infty)\) are also studied. Furthermore, based on the properties of this set, conditions ensuring the existence of quasisolutions and that of solutions of the minimization problem are established. These conditions differ according to \(r\neq\infty\) or \(r=\infty\).
nonlinear boundary value control problem
scientific article; zbMATH DE number 59778