Modeling and Control of Medical Systems

Physiological closed-loop control (PCLC) systems -autonomous therapy adjustments to regulate a physiological variable- are complex cyber-physical systems that involve interactions between patient monitors, therapeutic devices, complex patient physiology, and clinical users. In each of these, there are sources of variability and disturbances that can challenge the design, analysis, and evaluation of physiologic closed-loop controllers. Despite their obvious benefits, such as delivering improved therapies and reducing caregivers’ workload, PCLC systems are in early-stage development and still rare in the U.S. market due to the aforementioned challenges. Few existing examples are automated insulin delivery and automated anesthesia systems.

Research in CAM lab is focused on design, modeling, testing, and control of PCLC systems, especially for critical care application. We have designed and tested innovative methodologies for control-oriented dose-response modeling, non-invasive cardiac output monitoring, medical devices testing, and personalized drug delivery control for chronic medication therapies.

Chaos is a common phenomenon in multidimensional, nonlinear systems. Evolution of a chaotic system is sensitive to the initial conditions leading to specific properties such as unpredictability and topological transitivity. These properties make a chaotic system useful in many application areas, including secure communication, electronics, nonlinear optics, and signal processing.

Both "stabilization" and "synchronization" of chaotic systems have attracted a plethora of research in nonlinear systems control. Chaos stabilization is concerned with the design of a controller to remove the chaotic conduct and stabilize the chaotic system. Chaos synchronization entails the process of oscillating two chaotic systems, namely "drive" and "response" systems, in a synchronized manner. To this end, a proper control algorithm is needed to stabilize the synchronization error dynamics that arise from the mismatch between the drive and response systems to an equilibrium point such as the origin.

Research in CAM lab uses nonlinear control theory to design effective methodologies for stabilization and synchronization of chaotic systems. We have designed and tested a novel, nonlinear fuzzy Lyapunov exponents placement approach for the stabilization of Duffing oscillator and Lorenz chaotic circuit. We have also developed a hybrid control approach combining adaptive backstepping and fuzzy sliding mode control for the synchronization of two Rossler chaotic systems.

Robot manipulators have been widely used in many application areas, including industrial manufacturing, healthcare domains, mining operations, and space exploration technologies. Manipulators might comprise flexible components such as harmonic drives, where large gear ratios cause joint flexibility in the robotic system. Compared to their rigid counterparts, flexible-joint manipulators are substantially lighter and offer several advantages, including higher precision, lower energy consumption, and faster maneuverability. However, flexible manipulators’ operation and control are more challenging due to their uncertain, complex behavior and high degree of nonlinearity. As a result, effective control methods are needed to deal with the uncertainty and nonlinearity present in such manipulator systems.

Research in CAM lab is dedicated to tracking control and trajectory optimization of robot manipulators. We have developed a new optimal control approach, namely RBF-Galerkin, for direct trajectory optimization and costate estimation. This novel approach combings the radial basis function (RBF) interpolation with Galerkin projection to efficiently solve general optimal control problems. The RBF-Galerkin method incorporates arbitrary global RBFs along with the arbitrary discretization scheme offering a highly flexible framework for direct transcription. We also designed several advanced control algorithms for tracking control of flexible manipulators: i) A Sliding mode/H-Infinity Control approach, where the sliding mode controller stabilizes the nonlinear manipulator system and the H-infinity controller enhances the noise rejection capability of the system by reducing the total system nonlinearity; ii) A Backstepping/Reduced Active Disturbance Rejection Control (ADRC) approach, in which a reduced-order ADRC that uses an extended state observer (ESO) for the estimation of generalized disturbance of the robot manipulator was designed. The estimated states from ESO was then fed back to the backstepping controller that leverages a linear state space model to stabilize the system and track the movement of flexible manipulator.