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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This paper provides necessary conditions of optimality for optimal controlproblems with time delays in both state and control variables. Differentversions of the necessary conditions cover fixed end-time problems and, underadditional hypotheses, free end-time problems. The conditions improve onprevious available conditions in a number of respects. They can be regarded asthe first generalized Pontryagin Maximum Principle for fully non-smooth optimalcontrol problems, involving delays in state and control variables, only specialcases of which have previously been derived. Even when the data is smooth, theconditions advance the existing theory. For example, we provide a new`two-sided' generalized transversality condition, associated with the optimalend-time, which gives more information about the optimal end-time than the`one-sided' condition in the earlier literature. But there are improvements inother respects, relating to the treatment of initial data, specifying pasthistories of the state and control, and to the unrestrictive nature of thehypotheses under which the necessary conditions are derived.

Optimal Control Problems with Time Delays (Preliminary Version)