Feedback law with probabilistic certification for Propofol‐based control of BIS during anesthesia

Abstract

Summary This paper proposes a new control strategy for Propofol injection during anesthesia in patients undergoing surgery and where the Bispectral Index (BIS) is considered to be the regulated variable. The proposed control shows the nice feature of being completely independent of the knowledge of the pharmacokinetics that govern the diffusion of the drug. This paper also proposes a certification framework that gives a probabilistic guarantee regarding the containment of the BIS inside the desired interval as well as for the time needed for the BIS to be steered to this interval. Moreover, this certification is given for realistic (and hence very high) level of uncertainties on the parameters that define the unknown‐to‐the‐controller dynamics. This last feature is checked using a widely employed model.

Probabilistic performance validation of deep learning-based robust NMPC controllers

“…The result presented in the corollary has been published in a slightly different form in [52] and has been used in different control design problems. See, for example, [36], [37].…”

“…The sample complexity in this case does not depend on the dimension of the problem, but only of the required guaranteed probability of violation and confidence. Examples of probabilistic verification approaches in the context of control of nonlinear uncertain systems can be found, for example, in [25], [36] and [37]. These techniques have also been used for the probabilistic certification of the behaviour of off-line approximations of nonlinear control laws [38], [39].…”

Probabilistic performance validation of deep learning‐based robust NMPC controllers

“…The sample complexity in this case does not depend on the dimension of the problem, but only of the required guaranteed probability of violation and confidence. Examples of probabilistic verification approaches in the context of control of nonlinear uncertain systems can be found, for example, in References 26,37,38. These techniques have also been used for the probabilistic certification of the behaviour of off-line approximations of nonlinear control laws. 39,40 The main contribution of this paper, which extends the results from Reference 41, is the formulation of general closed-loop performance indicators that are not restricted to binary functions as in Reference 39 and can be computed simulating the closed-loop system with any given controller.…”

Extended tumor growth model for combined therapy

“…Application of system and control theory in physiological problems opens new perspectives in modern medicine. Modeling and control of BIS (bispectral index) in anesthesia [1]- [3], or modeling and control of blood glucose level in artificial pancreas applications [4]- [7] are well representative results of this interdisciplinary field. Modeling and control of tumor growth is an intensively researched area of physiological control as well aiming to automatize therapies and optimize treatment protocols [8]- [10].…”