October 2023 Accessibility and stabilization by infinite horizon optimal control with negative discounting
Fumihiko NAKAMURA
Author Affiliations +
Hokkaido Math. J. 52(3): 353-379 (October 2023). DOI: 10.14492/hokmj/2021-551

Abstract

The present paper investigates systems exhibiting two attractors, and we discuss the problem of steering the state from one attractor to the other attractor by our idea of associating with the stabilization problem an optimal control problem. We first formulate the steering problem and give partial answers for the problem in a two-dimensional case by using the ordinary differential equation based on the infinite horizon optimal control model with negative discounts. Furthermore, under some conditions, we verify that the phase space can be separated into some openly connected components depending on the asymptotic behavior of the orbit starting from initial points in their components. This classification of initial points suggests that the system enables robust stabilizable control. Moreover, we illustrate some numerical results for the control obtained by applying our focused system for the Bonhoeffer–Van der Pol model.

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Fumihiko NAKAMURA. "Accessibility and stabilization by infinite horizon optimal control with negative discounting." Hokkaido Math. J. 52 (3) 353 - 379, October 2023. https://doi.org/10.14492/hokmj/2021-551

Information

Received: 20 July 2021; Revised: 14 January 2022; Published: October 2023
First available in Project Euclid: 9 November 2023

Digital Object Identifier: 10.14492/hokmj/2021-551

Subjects:
Primary: 49J15
Secondary: 34D05

Keywords: Accessibility , infinite horizon , negative discounting , stabilization

Rights: Copyright c 2023 Hokkaido University, Department of Mathematics

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Vol.52 • No. 3 • October 2023
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