Control and anti-control of chaos based on the moving largest Lyapunov exponent using reinforcement learning

Han, Yanyan; Ding, Jianpeng; Du, Lin; Lei, Youming

doi:10.1016/j.physd.2021.133068

Cited by 11 publications

(2 citation statements)

References 29 publications

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“…In recent years, the DE-based method [15] has been shown to be an improvement of the UDE-based method; it has shown some advantages in handling some asymptotically unbounded external disturbances. But, for some asymptotically unbounded external disturbances, such as (A 2 t 2 + A 1 t + A 0 )e at , where A 0 , A 1 , A 2 are unknown constants, whereas a is a small known constant, there is still a lack of effective handling methods, even for the feedback based on deep reinforcement learning [16][17][18]. Thus, handling such asymptotically unbounded external disturbances has remained very challenging, which drove our current work.…”

Section: Introductionmentioning

confidence: 99%

Stabilization of the GLV System with Asymptotically Unbounded External Disturbances

Liu,

Guo

2023

Mathematics

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This paper investigates the stabilization of the generalized Lotka–Volterra (GLV) biological model, which is affected by the asymptotically unbounded external disturbances, and presents some new results. Firstly, two stabilizers are proposed for the nominal GLV system. Then, some appropriate filters are designed and applied to asymptotically track the corresponding disturbances. Based on these filters, two disturbance-estimator (DE)-based controllers are presented to cancel the corresponding disturbances. Compared to the existing results, the advantage of this paper is in handling the asymptotically unbounded external disturbances effectively. Finally, the correctness and effectiveness of the proposed results are verified by computer simulation.

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Section: Introductionmentioning

confidence: 99%

Stabilization of the GLV System with Asymptotically Unbounded External Disturbances

Liu,

Guo

2023

Mathematics

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“…Common bifurcation anti-control techniques are delayed feedback control method [13][14][15][16][17][18][19], washout filters approach [10,11], polynomial function method [20], and so on. Here, we shall point out that washout filters approach and polynomial function method are only applied to the anti-control of Hopf bifurcation for the integer-order dynamical systems.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation anti‐control technique in a fractional‐order stable finance model

Aouiti

et al. 2022

Asian Journal of Control

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Setting up differential models to give a description of the object economical phenomenon in the world today is very essential in economics and mathematics. In this current study, we are committed to the study on the anti‐control of Hopf bifurcation for a fractional‐order stable finance model. By virtue of a suitable washout filter controller involving time delay, we obtain a fractional‐order controlled finance model. Selecting the time delay as bifurcation parameter, we derive a new delay‐independent stability and bifurcation condition to assure that the involved fractional‐order controlled finance model is locally asymptotically stable and generates Hopf bifurcation around the equilibrium point. The investigation clearly manifests that the designed washout filter controller is a very effective means of bifurcation anti‐control. Ultimately, the obtained simulation figures and bifurcation diagrams are sufficiently presented to verify effectiveness for the proposed control technique. The established theoretical fruits have great significance in maintaining financial balance. Up to the present, the report on anti‐control technique of Hopf bifurcation for fractional‐order dynamical systems is quite rare. The research idea can also be applied to probe into the control issue of bifurcation and chaos for numerous other fractional‐order dynamical models in many areas.

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