Convergence of a feasible directions algorithm for relaxed controls in time-lag systems
We consider a class of time-lag optimal control problems involving control and terminal inequality constraints. A feasible direction algorithm has been obtained by \textit{K. L. Teo}, \textit{K. H. Wong}, and \textit{D. J. Clements} [ibid. 46, 295-317 (1985; Zbl 0548.49013)] for solving this class of optimal control problems. It was shown that any \(L_{\infty}\) accumulation points of the sequence of controls generated by the algorithm satisfy a necessary condition for optimality. However, such \(L_{\infty}\) accumulation points need not exist. The aim of this paper is to prove a convergence result, which ensures that the sequence of controls generated by the algorithm always has accumulation points in the sense of control measure, and these accumulation points satisfy a necessary condition for optimality for the corresponding relaxed problem.
control and terminal inequality constraints
scientific article; zbMATH DE number 3962593