Non-linear generalized predictive control (NLGPC) applied to muscle relaxant anaesthesia

The well-known generalized predictive control (GPC) algorithm is used to derive a discrete-time non-linear predictive controller for muscle relaxant anaesthesia, which has a Wiener structure representation, and which normally exhibits strong non-linearities as well as varying dead-time and lag dynamics owing to patient-topatient variability. The proposed controller minimizes the GPC quadratic performance index, taking into account the non-linear output predictions obtained using predictions of the linear part inferred using the inverse of the non-linear function. The minimization problem is solved using robust numerical search methods such as the golden section search method when NU= 1, the modified simplex method of Nelder-Mead when NU > 1 or genetic algorithms. Moreover, variations in the model dynamics are estimated using a recursive least-squares (RLS) estimation algorithm. The proposed scheme is shown to be superior to the linear GPC algorithm even in the case of significant mismatch between the assumed model nonlinearity and that of the actual system. The work forms the validation basis for future clinical trials on humans in operating theatre conditions.