Control-based method to identify underlying delays of a nonlinear dynamical system.

Area of Science:

• Control Systems Engineering
• Dynamical Systems Theory
• Nonlinear Dynamics

Background:

• Accurate identification of time delays is crucial for understanding and controlling complex dynamical systems.
• Existing delay identification methods often require detailed system structure information, limiting their applicability.
• Systems described by delayed ordinary differential equations (DODEs) present unique challenges for parameter estimation.

Purpose of the Study:

• To propose and validate novel stationary state control-based methods for identifying unknown time delays.
• To develop techniques applicable to systems described by DODEs without prior structural knowledge.
• To analyze the practical aspects and robustness of the proposed delay identification methods.

Main Methods:

• The proposed methods involve driving the system to a steady state.
• A perturbation is applied to the control signal to shift the steady state.
• Delays are identified by detecting abrupt deviations from stationarity.

Main Results:

• The developed methods successfully identify multiple time delays in systems without requiring structural information.
• Analysis confirms the reliability and robustness of the delay identification techniques, even in the presence of noise.
• Performance comparisons demonstrate the effectiveness of the proposed approaches.

Conclusions:

• Stationary state control-based methods offer a viable and effective approach for identifying delays in DODEs.
• The proposed techniques are broadly applicable and robust, addressing limitations of existing methods.
• Further investigation into practical applications like interaction delay identification is warranted.