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

Converging hierarchies of finite-dimensional semi-definite relaxations havebeen proposed for state-constrained optimal control problems featuringoscillation phe-nomena, by relaxing controls as Young measures. Thesesemi-definite relaxations were later on extended to optimal control problemsdepending linearly on the con-trol input and typically featuring concentrationphenomena, interpreting the control as a measure of time with a discretesingular component modeling discontinuities or jumps of the state trajectories.In this contribution, we use measures intro-duced originally by DiPerna andMajda in the partial differential equations litera-ture to modelsimultaneously, and in a unified framework, possible oscillation andconcentration effects of the optimal control policy. We show that hierarchiesof semi-definite relaxations can also be constructed to deal numerically withnoncon-vex optimal control problems with polynomial vector field andsemialgebraic state constraints.

Semi-definite relaxations for optimal control problems with oscillation and concentration effects