Optimal control on distributions

2017/02/09 by Constantin Udrişte, Udriste, Constantin
Computer Science · Engineering · Mathematics · #49J15 #49J20 #93C15 #93C20 #Advanced Differential Equations and Dynamical Systems #Control and Dynamics of Mobile Robots #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1702.02750

openalex publication_date 2017/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper studies (single-time and multitime) optimal control problems on a nonholonomic manifold (described either by the kernel of a Gibbs-Pfaff form or by the span of appropriate vector fields). For both descriptions we analyse: infinitesimal deformations and adjointness, single-time optimal control problems, multitime optimal control problem of maximizing a multiple integral functional, multitime optimal control problem of maximizing a curvilinear integral functional, Curvilinear functionals depending on curves, optimization of mechanical work on Riemannian manifolds. Also we prove that a nonholonomic system can be always controlled by uni-temporal or bi-temporal bang-bang controls.

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