I.Y. Sánchez Chávez, R. Morales-Menéndez, and S.O. Martínez Chapa (Mexico)
Linear Quadratic Control Problem, Optimal Control, Glucose-insulin dynamic behavior, Modelling
Optimal control allows the incorporation of functional con straints and requirements as a departure point for the de sign process. The linear quadratic control problem is a well characterized subset of this area and can be tailored for many applications. The continuous glucose control problem in a diabetic patient is addressed with the linear quadratic optimal con trol design principles. Continuous closed loop treatment of juvenile diabetes mellitus avoids the danger of hypo glycemia as a result of overcompensation, which is very likely to occur in traditional open loop insulin treatment. A glucose continuous control system is proposed. The glucose-insulin dynamic behavior is represented by Ackerman's linear state space model. This model considers the glucose level as the single output or monitored variable. 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 from this cost function. The control problem is tackled with two different ap proaches. First, the servocontrol approach verifies the out put against results available from previous works; how ever, an offset appears in the final glucose level. Second, the regulatory approach eliminates any offset in the final blood glucose concentration and minimizes transient glu cose level deviation and insulin supply. Both approaches are tested by simulation. By randomly changing the model parameters the robustness of the control law is examined. Results demonstrate the suitability of the optimization and regulatory approaches in biomedical engineering problems.
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