Optimal placement of sensor and actuator for controlling low-dimensional chaotic systems based on global modeling

Area of Science:

• Control Theory
• Nonlinear Dynamics
• Applied Mathematics

Background:

• Chaos control is crucial across various scientific and engineering fields.
• Existing methods often struggle with achieving global state control.
• System observability and controllability are key to effective chaos management.

Purpose of the Study:

• To propose a novel strategy for controlling chaotic systems.
• To achieve global state space observability and controllability.
• To enable precise feedback linearization for chaos control.

Main Methods:

• Optimal placement of sensors and actuators for global observability and controllability.
• Global modeling techniques to derive system dynamics.
• Feedback linearization based on the derived global model for control law design.
• Application to piecewise linear circuits like Carroll and Chua circuits.

Main Results:

• Demonstrated a method for achieving global observability and controllability.
• Successfully applied feedback linearization to chaotic circuits.
• Developed a continuous global model approximation for piecewise linear systems.
• Analyzed the sensitivity of the control strategy to system time constants.

Conclusions:

• Optimal sensor/actuator placement provides a robust framework for chaos control.
• The proposed method facilitates global state space control through feedback linearization.
• The technique is effective for complex nonlinear systems, including specific chaotic circuits.