Control of chaotic systems via reservoir computing approach.

Area of Science:

• Complex Systems Science
• Nonlinear Dynamics
• Control Theory

Background:

• Traditional chaos control relies heavily on precise analytical models of systems.
• Many real-world systems, especially industrial ones, lack such detailed analytical descriptions.
• Developing model-free control strategies for chaotic systems is crucial for broader applications.

Purpose of the Study:

• To propose and validate a data-driven approach for chaotic control.
• To demonstrate the efficacy of reservoir computing for modeling chaotic systems using observational data.
• To extend the applicability of chaos control to complex systems lacking analytical models.

Main Methods:

• Utilized reservoir computing to create a model from observational data of chaotic systems.
• Applied the Grebogi-Yorke algorithm to the reservoir computing model for control.
• Tested the approach on various chaotic and real-world systems.

Main Results:

• The reservoir computing model effectively characterized chaotic systems using only observational data.
• The Grebogi-Yorke algorithm successfully achieved synchronization, as indicated by dynamical variables.
• The approach demonstrated effectiveness across diverse chaotic and real-world system data.

Conclusions:

• The proposed data-driven method offers a viable alternative to traditional model-based chaos control.
• Reservoir computing provides a powerful tool for modeling and controlling complex chaotic dynamics.
• This research expands the potential of chaotic control in industrial and other complex settings.