English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We prove for a general optimal control problem that, in the absence of abnormal admissible extremals (solutions of a generalized Weierstrass E-condition), any control which is optimal in the set of original (ordinary) controls must also be optimal in the larger set of relaxed (measure-valued) controls. 1. We consider the model of an optimal control problem studied in (2). This model was found applicable, among others, to unilateral control problems defined by ordinary differential and multidimen­ sional integral equations (3), evasion problems (4), and conflicting control problems (5). For the sake of completeness, we begin by re­ stating the definition of this model. Let T and R be compact metric spaces and /x a positive and nonatomic Radon measure on T. We de­ note by rpm(R) the set of regular Borel probability measures on R endowed with the relative weak star topology of C(R)*, by (R the class of jLt-measurable functions on T to R (original control f unctions), and by S the set of ju-measurable functions on T to rpm(R) (relaxed control f unctions). We embed R in rpm(R) and (R in S by identifying each rÇzR with the Dirac measure at r. In turn, we view S as a subset of Ll(T, C(R))*, and endow it with the relative weak star topology, by identifying each (r£S with the functional <l>—*Jy<(dt)J<t>(t) (r)a(t) (dr). Now let R be the real line, 9C a real topological vector space, C a convex body in 9C, B a convex subset of a vector space (the set of con­ trol parameters)y m a positive integer, x = (x0, xi, X2)*SXB—>RXRm X 9C a given function, and

Normal control problems have no minimizing strictly original solutions