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Licensed Unlicensed Requires Authentication Published by De Gruyter 2017

15. Time-optimal control for a perturbed Brockett integrator

From the book Variational Methods

  • Jérôme Lohéac and Jean-François Scheid
https://doi.org/10.1515/9783110430394-015

Abstract

The aim of this paper is to compute time-optimal controls for a perturbation of a Brockett integrator with state constraints. Brockett integrator and its perturbations appear in many application fields. One of themdescribed in details in this paper is the swimming of micro-organisms.We present some key results for a fast and robust numericalmethod to compute time-optimal controls for the perturbation of a Brockett integrator. This numerical method is based on explicit formulae of time-optimal controls for the Brockett integrator. The methodology presented in this paper is applied to the time-optimal control of a micro-swimmer.

© 2016 Walter de Gruyter GmbH, Berlin/Munich/Boston
From the book
Variational Methods
Variational Methods

Chapters in this book (20)

Frontmatter
Contents
Part I
1. Second-order decomposition model for image processing: numerical experimentation
2. Optimizing spatial and tonal data for PDE-based inpainting
3. Image registration using phase–amplitude separation
4. Rotation invariance in exemplar-based image inpainting
5. Convective regularization for optical flow
6. A variational method for quantitative photoacoustic tomography with piecewise constant coefficients
7. On optical flow models for variational motion estimation
8. Bilevel approaches for learning of variational imaging models
Part II
9. Non-degenerate forms of the generalized Euler–Lagrange condition for state-constrained optimal control problems
10 The Purcell three-link swimmer: some geometric and numerical aspects related to periodic optimal controls
11. Controllability of Keplerian motion with low-thrust control systems
12. Higher variational equation techniques for the integrability of homogeneous potentials
13. Introduction to KAM theory with a view to celestial mechanics
14. Invariants of contact sub-pseudo-Riemannian structures and Einstein–Weyl geometry
15. Time-optimal control for a perturbed Brockett integrator
16. Twist maps and Arnold diffusion for diffeomorphisms
17. A Hamiltonian approach to sufficiency in optimal control with minimal regularity conditions: Part I
Index
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