Linear quadratic control problem in biomedical engineering

Abstract

Abstract Optimal control allows the incorporation of functional constraints and requirements as a departure point for the design process. The glucose continous control problem in a diabetic patient is addressed with the linear quadratic optimal control design principles. A glucose control system is proposed. The glucose-insulin dynamics is represented by the Ackerman's model. This model considers the glucose level as the single output, so a state space observer is used to estimate the blood insulin level. The cost function is defined in quadratic terms of the exceeding glucose level and the amount of supplied insulin. An optimal control law is generated under servocontrol and regulatory approaches. Robustness of the control law in each case is examined by a Monte Carlo simulation. Results demonstrate the suitability of the optimization and regulatory approaches in biomedical engineering problems.