Applied & Computational Mathematics seminar: Finite-Time Targeting Control in Weakly Stable Dissipative Systems -- Spontaneous Transition of Optimal Perturbation Patterns –

Speaker:  Yoshitaka Saiki, Hitotsubashi University, Japan

Title:  Finite-Time Targeting Control in Weakly Stable Dissipative Systems
-- Spontaneous Transition of Optimal Perturbation Patterns --

Abstract:   Understanding finite-time sensitivity is central to high-dimensional
dissipative systems, from fluid dynamics to atmospheric science, where
direct control remains a fundamental challenge. While classical
optimal perturbation theory focuses on maximal growth problems, many
realistic interventions are inherently directional: the objective is
to steer a system toward a prescribed target state at a finite time
using a limited initial perturbation.

In this talk, I present a systematic study of finite-time targeting in
weakly stable dissipative systems. Using a spatially extended coupled
map lattice as a toy model for Rayleigh–Bénard convection, we
demonstrate that varying only the allowable magnitude of the initial
perturbation induces a sharp qualitative transition in the structure
of optimal perturbations. The optimal patterns switch abruptly from
spatially ordered (coherent) structures to highly complex (incoherent)
ones.

We show that the coherent regime can be understood analytically
through a linearized formulation of the finite-time targeting problem.
The optimal perturbation is characterized by a singular value
decomposition of the finite-time evolution operator, which reveals
that non-leading singular modes can dominate optimality due to their
alignment with the target. Beyond a critical perturbation magnitude,
however, linear predictability breaks down. In this regime, nonlinear
phase-space geometry becomes relevant for shaping optimal
perturbations, in particular through the influence of basin boundaries
associated with unstable invariant states, even in the absence of
actual basin switching.

More broadly, this work highlights a generic mechanism: when
objectives are directional and interventions are small, optimal
influence is governed as much by geometry as by growth.
This is a joint work with Natsuki Tsutsumi, Hibiki Kato, Masato Hara,
Miki U. Kobayashi, and Tatsuo Yanagita.

 

Time:  Friday, February 13, 1:30pm – 2:30pm
Place:  Exploratory Hall, room 4106