Data-driven Koopman Linear Quadratic Regulator Control of Microbubble Oscillations

Encapsulated microbubbles (EMBs) are used in biomedicine for both diagnostic and therapeutic purposes that include ultrasound imaging and targeted drug delivery. A data-driven method to control the oscillations of EMBs using the applied acoustic field is presented based on Koopman operator theory, which is a method for transforming a nonlinear dynamical system on a state space into a linear system on an infinite-dimensional function space. This method preserves the underlying nonlinear dynamics of the system, and the function spaces can be approximated through data-driven methodologies, which enables the application of classical linear control strategies to the nonlinear system. Here, we apply a Koopman linear quadratic regulator (KLQR) to control the nonlinear oscillations of a EMB through the applied acoustic field. Results are presented that demonstrate the effectiveness of the modified KLQR controller in driving the EMB to follow arbitrarily prescribed radial oscillations and stabilize at nonequilibrium radius.