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 this work, we consider optimal control problems for mechanical systems onvector spaces with fixed initial and free final state and a quadratic Lagrangeterm. Specifically, the dynamics is described by a second order ODE containingan affine control term and we allow linear coordinate changes in theconfiguration space. Classically, Pontryagin's maximum principle givesnecessary optimality conditions for the optimal control problem. For smoothproblems, alternatively, a variational approach based on an augmented objectivecan be followed. Here, we propose a new Lagrangian approach leading toequivalent necessary optimality conditions in the form of Euler-Lagrangeequations. Thus, the differential geometric structure (similar to classicalLagrangian dynamics) can be exploited in the framework of optimal controlproblems. In particular, the formulation enables the symplectic discretisationof the optimal control problem via variational integrators in a straightforwardway.

A new Lagrangian approach to control affine systems with a quadratic Lagrange term