Abstract : This two part mini-symposium addresses theoretical aspects of optimisation of systems governed by ODEs and applications. Optimal control and the associated analysis indeed provides a framework general enough to cover the Riemannian case, and gradient flows on such manifolds, as well as the Finslerian one - in particular Zermelo type problems. It is also instrumental to deal with more singular situations involving for instance Fuller and turnpike phenomena. Two privileged domains of applications are considered: space mechanics, in connection with dynamical system analysis for mission design, and biology with a focus on micro-swimmers and bacterial growth.
[04845] A variational approach for modelling and optimal control of electrodynamic tether motion
Format : Talk at Waseda University
Author(s) :
Yana Valentinova Lishkova (University of Oxfordrsity of Oxford)
Mai Bando (Kyushu University)
Sina Ober-Blöbaum (Paderborn University)
Abstract : We present a novel variational model for 6DOF spacecraft dynamics equipped with an electrodynamic tether in circular restricted three-body environment and use it to perform an optimal orbit transfer with simultaneous orbit and attitude control. We discuss the advantages of the suggested variational approach and develop an alternative multirate formulation of the model and OCP, investigating the extent to which such reformulations can reduce the computational cost of simulating and optimally controlling spacecraft in CR3BP.
[04761] The Role of Stable Manifolds in Optimal Control under Stochastic Noise
Format : Talk at Waseda University
Author(s) :
Mai Bando (Kyushu University)
Shohei Morimitsu (Kyushu University)
Takuro Nishimura (Kyushu University)
Shinji Hokamoto (Kyushu University)
Abstract : This study investigates the optimal control around a hyperbolic fixed point under stochastic noise. For a deterministic system without noise, it is known that the stable manifold of a hyperbolic fixed point is the solution to the minimum-energy problem with infinite horizon. We analyze the structure of the optimal control under a stochastic noise based on path integral approach and investigate the role of the stable manifold of the hyperbolic fixed point.
[04228] Second-order averaging of time-optimal low-thrust orbital transfers
Format : Talk at Waseda University
Author(s) :
Lamberto Dell'Elce (Inria & Université Côte Azur)
Abstract : This work offers a numerical methodology to solve low-thrust orbital transfer problems. After detailing necessary conditions for optimality stemming from the Pontryagin maximim principle, a numerical methodology based on the averaging of the extremal flow of the optimal control hamiltonian is proposed. First, a one-parameter family of averaged solutions is obtained. Second, perturbations of these solutions associated to both short-periodic variations and second-order terms are computed. Finally, the magnitude of the thrust-to-mass ratio is identified by reconstructing a first-order approximation of the fast variables from the averaged solution.
[03208] Optimization on manifolds by Riemannian gradient methods
Format : Talk at Waseda University
Author(s) :
Hiroyuki Sato (Kyoto University)
Abstract : In this talk, we will discuss optimization on Riemannian manifolds. After introducing examples of manifold optimization problems, some recent results by the speaker will be presented. In particular, the Riemannian conjugate gradient method is a simple first-order method, which does not use the Hessian but only the gradient of the objective function, and it shows much faster convergence performance than the Riemannian steepest descent method. Reference: H. Sato, Riemannian Optimization and Its Applications, Springer, 2021.
[04787] Curvature related properties of Finsler manifolds and applications
Format : Talk at Waseda University
Author(s) :
Sorin Sabau (Tokai University)
Abstract : Finsler manifolds are important generalizations of Euclidean and Riemannian ones with applications in different domains of mathematics, physics and engineering. In the present talk we are going to present some recent results concerning Finsler connections, curvature and relation with statistical models in the real world. We suggest possible development of information geometry on Finsler manifolds that would allow a wide range of applications.
[03504] Optimal microswimmer control and a microfluidic control example
Format : Talk at Waseda University
Author(s) :
Clement Moreau (RIMS, Kyoto University)
Abstract : Microscale swimmers are becoming increasingly prevalent. A natural question that arises from such swimmers, particularly those synthetic swimmers with targeted applications, is that of guidance and control.
The purpose of this presentation is to give an overview of the results of optimal control theory in the study of micro-swimming organisms and devices. As an illustrative example, I will present time-optimal trajectories for a model of microfluidic control representing a swimmer guided through the external flow generated by a neighboring wall.
[04894] Control Problems inspired by Biological Phenomena
Format : Talk at Waseda University
Author(s) :
Tetsuya J. Kobayashi (Institute of Industrial Science, UTokyo)
Takehiro Tottori (The University of Tokyo)
Shuhei A Horiguchi (The University of Tokyo)
Abstract : In order to understand the design principles of biological systems, which sometimes demonstrate more efficient and sophisticated behaviors than engineering systems, the notion of control is indispensable. However, the control theories developed in the engineering domain under their standard assumptions can not necessarily be appropriately applied to biological phenomena, resulting in limited applicability to biological systems. In this presentation, we will discuss several extended control theories inspired by biological phenomena and their potential applications.
[04045] Control in biology: topics in bacterial growth
Abstract : We consider bacteria whose internal dynamics is modelled by the so-called self-replicator equations. This low dimensional ODE system accounts for the behaviour of the cell. The control mimics the allocation process of the cell that decides to use substrate either for gene expression or for its metabolism. Another control can be added to model an external action on a the bio-engineered cell; thanks to optogenetics, one can for instance use light to trigger the production by the cell of a metabolite of interest. Several criteria are of interest here, particularly growth maximisation, or metabolite production. Pontrjagin maximum principle allows to analyse these problems, revealing two characteristic features of these optimal control problems: Fuller phenomenon and turnpike behaviour. Some symbolic-numeric results are given to illustrate these.
Joint work with colleagues from Biocore, McTAO and MICROCOSM Inria teams. Support from the ANR is acknowledged (Maximic project).
