Selection of kinematic requirements for RFPT-based adaptive anaesthesia control

The automatic control of the level of hypnosis is a significant part of anaesthesia during surgical operations. The prevalent patient models consist of a four variable set of ordinary differential equations with a driving term, the Propofol infusion rate. One of the directly observable quantities is the Bispectral Index that is related to one of the state variables by a nonlinear function with patient-dependent parameters that have quite significant interpatient variability and normally cannot be known in advance. Furthermore, this index can suffer abrupt variations during the surgical operations. This fact makes the application of classical control approaches difficult because they operate with state feedback gains and state observers. The significant model uncertainties need either robust or adaptive solutions. A novel alternative of the Lyapunov function based adaptive control design, i.e. the Robust Fixed Point Transformation (RFPT)-based adaptive control can solve such problems by replacing the complicated state space model with a simple affine function instead of the use of state observers. This method strictly separates the kinetic and dynamic aspects of the controlled motion so allows arbitrary kinetic prescription for the tracking error relaxation. Via numerical (“in silico”) simulations it is shown how the four investigated plausible kinetic options (namely the “PD-type”, “PID-type”, “Error Metrics-based PD-type”, and “Error Metrics-based PID-type” prescribed tracking error relaxation) concern the quality of the control. It is found that two different options, the “PD-type” and the “PID-type” ones, have almost equally good results while the other ones seem to be less efficient.