Regensburg 2025 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 27: Poster: Nonlinear Dynamics, Pattern Formation, Granular Matter
DY 27.6: Poster
Mittwoch, 19. März 2025, 15:00–18:00, P4
Optimal Control of Fractional Bistable System — •Finn Biesterfeldt1, Andreas Rauh2, and Alexander K. Hartmann1 — 1Institut für Physik, Carl von Ossietzky Universität Oldenburg, 26111 Oldenburg, Germany — 2Department für Informatik, Carl von Ossietzky Universität Oldenburg, 26111 Oldenburg, Germany
In this work, a classic bistable system in continuous time and space and described by an ordinary integer-order differential equation is generalized to fractional order using the principles of Fractional Calculus. This results in an intrinsic memory effect and the time evolution depends on the full history of its prior configurations. In numerical simulations we observe that depending on the initial conditions, the system drives towards one of two possible fixed points of the integer order system. Initializing the system with a non-constant history leads to a complex time evolution that is highly dependent on the fractional order. In this study, the non-constant history can be interpreted as an external influence or control input that drives the system from one fixed point to the other. Influenced by the fractional order, the system may converge back to the initial fixed point. The optimal control strategy for transitioning the system from one to the other fixed point is computed numerically, revealing a dependence on the fractional order of the system.
Keywords: Fractional Dynamics; Optimal Control; Memory Effect; Dynamic System; Bistable