Brandi, Primo; Salvadori, Anna On measure differential inclusions in optimal control theory. (English) Zbl 1028.49002 Rend. Semin. Mat., Torino 56, No. 4, 69-86 (1998). In this paper the authors consider the following measure differential inclusion problem \[ \frac{d\mu _a}{d\lambda}(t)\in Q(t),\quad\lambda\text{-a.e. }t\in I, \]\[ \frac{d\mu _s}{d|\mu _s|}(t)\in [Q(t)]_\infty,\quad \mu_s\text{a.e. }t\in I, \] where \(\mu=\mu_a+\mu_s\) is a Borel measure on \(I\subset \mathbb{R}\), \(\mu_a\) is the absolutely continuous part of \(\mu\) with respect to the Lebesgue measure \(\lambda\), \(\mu_s\) the singular part, \(t\to Q(t)\) a multifunction with \(Q(t)\) a non-empty closed and convex subset of \(\mathbb{R}^n\) and \([Q(t)]_\infty\) the asymptotic cone of \(Q(t)\). The main result of this paper is a closure result under weak convergence of measure, and it is based on the proof of the equivalence of the strong and weak formulation of the problem. In addition an application of optimal control problems in the BV setting is given. Reviewer: Michele Miranda (Lecce) Cited in 2 Documents MSC: 49J24 Optimal control problems with differential inclusions (existence) (MSC2000) 49J45 Methods involving semicontinuity and convergence; relaxation Keywords:optimal control; measure differential inclusions; weak convergence of measure PDFBibTeX XMLCite \textit{P. Brandi} and \textit{A. Salvadori}, Rend. Semin. Mat., Torino 56, No. 4, 69--86 (1998; Zbl 1028.49002) Full Text: EuDML