# Fractional-Order Closed-Loop Model Reference Adaptive Control for Anesthesia
## 3 Anesthesia
### Challenges  
Drug responses in humans are the result of integrated effects, including signal amplification and dampening mechanisms at cellular, tissue, and physiological system levels, and the pharmacodynamic responses can be therapeutic, toxic, or lethal. In anesthesiology, it is easy to observe that the response to the same drug dose varies widely among patients. Part of the process of delivering anesthesia is titrating a drug dose to provide optimal therapy for a specific patient, particularly when the drug has a significant level of toxicity. At the same time, the anesthesiologist must know the dosing ranges that are appropriate for broad populations of patients to provide dosing guidelines. The classical PK/PD models are coarse abstractions of a real distribution and elimination process. Still, these models describe the measured and observed concentrations. Another more complex type of model exists, called physiologically-based models [63]. With these models, it is possible to have more information available, for example, the influence of changes in cardiac output and organ blood flow on the time course of the concentration in the blood and various organs and tissues. Unfortunately, the development of such accurate models is expensive and can only be performed on animals. Furthermore, these accurate models are complex and have too many variables and parameters to be useful in the development of controllers. The potential benefits of a closed-loop anesthesia delivery are more consistent drug administration, less inter- and intra-patient variability, less over- and under-dosages, faster control action to unexpected arousal (perturbation rejection), smaller quantities of drug usage, faster recovery of the patient, better hemodynamic control, and less hypotension during the induction of anesthesia. These factors are what keeps the interest in the control community to design reliable control schemes. Moreover, this problem is still considered an open problem. The current state of the art understanding of the unconsciousness and the mechanisms of drug-induced unconsciousness is limited. Therefore, is very challenging to translate these little-known mechanisms into an accurate mathematical model. One of the most critical challenges in the design of high-performance controllers for anesthetic drug delivery is the lack of accurate models. Another challenge is the identification of a model from clinical data, as it has been shown [64] that the information available in the operating room (infusion rate of the drug and BIS index usually) is insufficient to identify a full-order PK/PD model. The excitation in the input signal is not sufficiently frequency rich and is not able to excite all modes in the model, because this input cannot be selected freely. Additionally, this model has a Wiener structure. Therefore, the task of identifying an individualized model online is very challenging. Linear and nonlinear reduced-order model structures have been proposed to improve the identifiability and the control synthesis of the anesthesia process. In [13], the authors presented a piecewise linear model, with which they used different LTI models to represent different phases of the process. For example, one model was used for the induction phase and another for the maintenance phase. Then, they synthesized a controller for each phase, similar to gain scheduling schemes. In reference [65], a standard PK/PD model was proposed in which the authors assumed that only the PD parameters were responsible for the inter-patient variability, and an extended PK model was used and the model was linearized with the PD parameters identified via a Kalman filter. A first-order plus time-delay was proposed in reference [10]. Here, the PK parameters are fixed, the Hill curve is linearized around an operating point, and the PD parameters are calculated using a standard least square algorithm. In [66], a reduced-order model obtained using model reduction technics was obtained.