Weight Matrix Syntheses Using the Controllability Gramian for LQR Anaesthesia Control

When it comes to the process of designing a control law for general anaesthesia there are many challenges. One of them is the nonlinear mapping of the output and the problem of a feasible input trajectory. From the point of view of the mathematical model, the internal states are linear, only the output has nonlinear terms. The current work presents a decomposition of the standard Pharmacokinetic-Pharmacodynamic model, and an approach to control the effect of the drugs on the patient. In this manner a suitable linear control law can be determined. It is also presented a framework for computing the weight matrices Q and R used for the Linear Quadratic Regulator method based on the Controllability Gramian of the system. The paper proposes and compares three newly developed methods, taking into account as performance the evolution of the Bispectral Index as well as the total input energy required to reach these levels.