  Closed loop anesthesia delivery (CLAD) systems can help anesthesiologists
efficiently achieve and maintain desired anesthetic depth over an extended
period of time. A typical CLAD system would use an anesthetic marker,
calculated from physiological signals, as real-time feedback to adjust
anesthetic dosage towards achieving a desired set-point of the marker. Since
control strategies for CLAD vary across the systems reported in recent
literature, a comparative analysis of common control strategies can be useful.
For a nonlinear plant model based on well-established models of compartmental
pharmacokinetics and sigmoid-Emax pharmacodynamics, we numerically analyze the
set-point tracking performance of three output-feedback linear control
strategies: proportional-integral-derivative (PID) control, linear quadratic
Gaussian (LQG) control, and an LQG with integral action (ILQG). Specifically,
we numerically simulate multiple CLAD sessions for the scenario where the plant
model parameters are unavailable for a patient and the controller is designed
based on a nominal model and controller gains are held constant throughout a
session. Based on the numerical analyses performed here, conditioned on our
choice of model and controllers, we infer that in terms of accuracy and bias
PID control performs better than ILQG which in turn performs better than LQG.
In the case of noisy observations, ILQG can be tuned to provide a smoother
infusion rate while achieving comparable steady-state response with respect to
PID. The numerical analyses framework and findings, reported here, can help
CLAD developers in their choice of control strategies. This paper may also
serve as a tutorial paper for teaching control theory for CLAD.
