Koopman linear quadratic regulator control of an acoustically driven encapsulated microbubble

Area of Science:

• Biomedical Engineering
• Nonlinear Dynamics
• Control Theory

Background:

• Encapsulated microbubbles (EMBs) are crucial for biomedical applications like ultrasound imaging and drug delivery.
• Controlling the nonlinear dynamics of EMBs is challenging but essential for precise applications.
• Existing control methods struggle with the complex behavior of EMBs in biological environments.

Purpose of the Study:

• To develop a data-driven method for controlling encapsulated microbubbles (EMBs) using acoustic fields.
• To apply Koopman operator theory and Koopman linear quadratic regulator (KLQR) for precise EMB manipulation.
• To investigate and overcome the unique dynamic challenges posed by EMBs, including their slow manifold.

Main Methods:

• Utilized Koopman operator theory to linearize the nonlinear dynamics of EMBs.
• Designed acoustic control signals using a Koopman linear quadratic regulator (KLQR) based on the Marmottant model.
• Analyzed the impact of EMB encapsulation and slow manifold dynamics on control performance.

Main Results:

• Demonstrated effective control of EMBs to achieve specific behaviors like subharmonic resonance amplification and quasiperiodic oscillations.
• Identified that the slow manifold in EMB dynamics presents unique control challenges.
• Showcased the necessity of carefully constructed Koopman eigenfunctions to capture relevant dynamics for robust control.

Conclusions:

• Koopman operator theory provides a powerful framework for controlling nonlinear systems like EMBs.
• The KLQR controller is effective in driving EMBs to target behaviors, despite dynamic complexities.
• Addressing the slow manifold dynamics is critical for successful acoustic control of encapsulated microbubbles in biomedical applications.