Luenberger-Like Observers for Nonlinear Time-Delay Systems with Application to the Artificial Pancreas: The Attainment of Good Performance

Abstract

Analysis and control of time-delay systems has gained increasing interest in the last decades, due to the effectiveness of delay-differential equations in modeling a wide range of physical and engineering frameworks, such as ecological systems, industrial processes, telerobotic systems, earth controlled satellite devices and biomedical engineering. A further great impulse has been recently given by networked and distributed control, which may naturally induce non-negligible and possibly time-varying delays in the input/output channels. As in the case of systems described by ordinary differential equations, a crucial point in most advanced control approaches, such as optimal and robust control, is the possibility to solve the so-called observer problem, that is the design of algorithms that provide full information on the state of the system by real-time processing of few measurements. The reader can refer to the recent edited book on nonlinear delay systems and references therein [1]. Nonlinear time-delay systems are characterized by the presence of one or multiple delays in the input, state, or measurement equations. In particular, delays in the state equations occur

A revised Sorensen model: Simulating glycemic and insulinemic response to oral and intra-venous glucose load

“…Much previous work addressed the need of developing glucose/insulin models, with different levels of complexity, for a variety of reasons, such as the study of insulin sensitivity or for controlled automatic insulin delivery (artificial pancreas) [7][8][9][10][11][12]. These models were to be identified on each single patient and had therefore to incorporate the relevant physiological mechanisms in a simplified fashion.…”

“…With the goal of maintaining glucose levels inside a narrow range of values, a number of closed-loop control methods have been designed, often relying on a limited or sparse number of observations, approach that is often referred to with the general term artificial pancreas (see e.g. [7][8][9][10][11][12] and references therein); these systems base their efficacy, in terms of in-silico testing, on reliable mathematical models of glucose homeostasis.…”

Dominant‐pole placement for predictor synthesis

“…2 In population studies, delays in the application of social distancing measures and the data recollection process make the susceptible, infectious, and recovered epidemic model more realistic. 3 Similarly, a delay is observed in the glucose-insulin model 4 as the plasma glucose concentration does not respond instantly to insulin level changes. While small input delays may often be neglected, larger ones are detrimental to the closed-loop system performance and can cause oscillations or instability.…”

Novel Robust Estimation-Based Control of One-Sided Lipschitz Nonlinear Systems Subject to Output and Input Delays

“…Various practical systems, especially those influenced by transmission, transportation, or inertial phenomena, incorporate delayed differential equations. Conventional control methods described in the literature are not directly applicable to such delayed dynamics systems, and hence have received considerable attention from researchers for linear and nonlinear systems [20][21][22][23][24][25][26][27][28][29]. Time delay can be observed in input, output, or both.…”