Pith. sign in

REVIEW 1 cited by

Pontryagin Maximum Principle - a generalization

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 0905.2767 v2 pith:YRLFQY7M submitted 2009-05-17 math.OC math.DG

Janusz Grabowski , Michal Jozwikowski This is my paper · ORCID
classification math.OCmath.DG
keywords algebroidscontrolmaximumoptimalpontryaginprinciplealmostanalytical
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

The fundamental theorem of the theory of optimal control, the Pontryagin maximum principle (PMP), is extended to the setting of almost Lie (AL) algebroids, geometrical objects generalizing Lie algebroids. This formulation of the PMP yields, in particular, a scheme comprising reductions of optimal control problems similar to the reduction for the rigid body in analytical mechanics. On the other hand, in the presented approach the reduced and unreduced PMPs are parts of the same universal formalism. The framework is based on a very general concept of homotopy of measurable paths and the geometry of AL algebroids.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Optimal control problems on the co-adjoint Lie groupoids

    math.OC 2024-11 reject novelty 3.0 of 10

    Any right-invariant optimal control problem on a Lie groupoid is claimed to reduce to one on its co-adjoint Lie algebroid, but the key step is cited, not proven.

Pith tools