## 4 Model Predictive Control Algorithms  
Also referred to as moving horizon or receding horizon control, model predictive control (MPC) is a form of control in which the current control action is obtained by solving, at each sampling point, a finite horizon optimal control problem, using the current state of the system as the initial state. This differs considerably from classic PID or other conventional algorithms that use offline control law computation; MPC systems allow parameter optimization while the algorithm is on-line and running. As a result, in a real-time continuous fashion, an MPC algorithm identifies solutions for control problems for the current state of the system and at every unit time interval, rather than providing a single solution for all points along the timeline. Also, using a finite horizon helps to provide the optimal solution for the control problem in a reasonable time frame, rather than using infinite horizon prediction, such as employed in H-infinity systems [23]. These characteristics permit MPC to control systems with long time delays and open-loop qualities, and these characteristics are quite relevant to the management of insulin delivery for glycemic control in subjects with type 1 diabetes [24]. [PERSON] et al developed a compartment model of the glucoregulatory system including subsystem models of carbohydrate absorption from the gut and insulin absorption subcutaneously. The controller uses Bayesian parameter estimation to determine time-varying model parameters. A moving target trajectory facilitates slow, controlled normalization of elevated glucose levels and faster normalization of low glucose values [23]. The Advanced Insulin Infusion using a Control Loop (ADICOL) project [5] initially tested the MPC algorithms in an '_in silico_' environment in the hopes of developing a treatment system for subjects with type 1 diabetes. In a randomized, controlled trial of 60 patients studied during cardiac surgery in surgical care units across Europe, continuous insulin infusion therapy was evaluated under control of protocol-specific guidelines versus an MPC algorithm. The MPC algorithm showed greater ability to maintain glycemic control [24]. This trial provides promising and encouraging results that suggest the potential for safe and efficient glycemic control in an intensive care setting. Further trials in both surgical and medical intensive care settings have provided similar results with MPC algorithm-controlled glucose systems [25]. The intensive care unit is an attractive location for such studies, given the close oversight of patients/subjects by health care personnel. Figure 2: Model Predictive Control: The graph shows the change in actual glucose, the model-predicted change in glucose and the insulin infusion rates during three horizon segments. Upon reaching the first horizon actual glucose fails to decline to the predicted target, thus the insulin infusion rate is increased (for example by lowering the estimate for insulin sensitivity). At the second horizon, glucose has declined below the target, thus insulin infusion rate is reduced. At the third horizon on the actual glucose has reached the predicted target value and the estimate of insulin sensitivity remains unchanged. In terms of the concepts used in this and other MPC studies, it is important to note that MPC is an adaptive system and adapts itself to the input-output relationship observed during tight glucose control. That is, an incoming glucose measurement is used by the model to update model parameters such as insulin sensitivity, in view of previously administered insulin and glucose intake. MPC used in the setting of intravenous (IV) insulin delivery is simpler than the setting of subcutaneous insulin due to the fact that a submodel describing insulin absorption from the subcutaneous depot is not needed.