15. Time-optimal control for a perturbed Brockett integrator
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Jérôme Lohéac
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.
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.
Chapters in this book
- Frontmatter I
- Contents V
-
Part I
- 1. Second-order decomposition model for image processing: numerical experimentation 5
- 2. Optimizing spatial and tonal data for PDE-based inpainting 35
- 3. Image registration using phase–amplitude separation 84
- 4. Rotation invariance in exemplar-based image inpainting 108
- 5. Convective regularization for optical flow 184
- 6. A variational method for quantitative photoacoustic tomography with piecewise constant coefficients 202
- 7. On optical flow models for variational motion estimation 225
- 8. Bilevel approaches for learning of variational imaging models 252
-
Part II
- 9. Non-degenerate forms of the generalized Euler–Lagrange condition for state-constrained optimal control problems 295
- 10 The Purcell three-link swimmer: some geometric and numerical aspects related to periodic optimal controls 314
- 11. Controllability of Keplerian motion with low-thrust control systems 344
- 12. Higher variational equation techniques for the integrability of homogeneous potentials 365
- 13. Introduction to KAM theory with a view to celestial mechanics 387
- 14. Invariants of contact sub-pseudo-Riemannian structures and Einstein–Weyl geometry 434
- 15. Time-optimal control for a perturbed Brockett integrator 454
- 16. Twist maps and Arnold diffusion for diffeomorphisms 473
- 17. A Hamiltonian approach to sufficiency in optimal control with minimal regularity conditions: Part I 496
- Index 517
Chapters in this book
- Frontmatter I
- Contents V
-
Part I
- 1. Second-order decomposition model for image processing: numerical experimentation 5
- 2. Optimizing spatial and tonal data for PDE-based inpainting 35
- 3. Image registration using phase–amplitude separation 84
- 4. Rotation invariance in exemplar-based image inpainting 108
- 5. Convective regularization for optical flow 184
- 6. A variational method for quantitative photoacoustic tomography with piecewise constant coefficients 202
- 7. On optical flow models for variational motion estimation 225
- 8. Bilevel approaches for learning of variational imaging models 252
-
Part II
- 9. Non-degenerate forms of the generalized Euler–Lagrange condition for state-constrained optimal control problems 295
- 10 The Purcell three-link swimmer: some geometric and numerical aspects related to periodic optimal controls 314
- 11. Controllability of Keplerian motion with low-thrust control systems 344
- 12. Higher variational equation techniques for the integrability of homogeneous potentials 365
- 13. Introduction to KAM theory with a view to celestial mechanics 387
- 14. Invariants of contact sub-pseudo-Riemannian structures and Einstein–Weyl geometry 434
- 15. Time-optimal control for a perturbed Brockett integrator 454
- 16. Twist maps and Arnold diffusion for diffeomorphisms 473
- 17. A Hamiltonian approach to sufficiency in optimal control with minimal regularity conditions: Part I 496
- Index 517
