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

In optimal control problems of control-affine systems, whose solutions arebang-bang or singular type, verification of optimality using theHamilton-Jacobi-Bellman (HJB) equation involves the computation of partialderivatives of switching times and switching states with respect to initialconditions (time and state). In this paper, we establish a formula for thepartial derivatives of ordinary differential equations (ODE) flows with respectto initial conditions, which is more suitable for using in HJB equation thansuch provided by the classical theory of ODE. We apply the obtained results tothe sensitivity analysis of hitting time and state of a reachable set, that inan optimal control problem can represent a switching locus.

A Hamilton-Jacobi approach of sensitivity of ODE flows and switching points in optimal control problems