Regularity properties of optimal controls with application to discrete approximation
The paper is an improvement of the recent result of \textit{A. L. Dontchev} [SIAM J. Control Optimization 34, No. 4, 1315-1328 (1996; Zbl 0851.49023)] about discrete approximations under uniform coercivity conditions on the discrete solutions for differential equations. Moreover, the regularity is further specified by Lipschitz continuity. The form of \( L_{\infty}\)-terms for the optimal control problem is proceeding along the essential limit concept for \(L_{\infty}\)-functions (Section 2) and the description of structure of an optimal control based on a finite number of Lipschitz continuous arcs (Section 3). The final section is devoted to the above mentioned improvement and discussions about the expected convergence properties of the Euler approximation with jump discontinuities located at resident grid points w.r.t. the sequence of discretizations.
scientific article; zbMATH DE number 1347772