Improving continuous–discrete interval observers with application to microalgae-based bioprocesses

Estimation of neutral lipid and carbohydrate quotas in microalgae using adaptive interval observers

“…Therefore, in direct consequence of Proposition 1, this system is a framer for System (8), with a near-optimal convergence of the error given that the gains θ + i (t) and θ − i (t) will converge towards the optimal values defined in Section 3.3 (see Proposition 2).…”

“…Based on the theory of positive differential systems [5], this robust state estimation technique is of particular interest for bioprocesses, which suffer from high uncertainties (on the inputs, measurements and model dynamics) and the lack of on-line measurements. Interval observers have been successfully applied to biological systems [6,7,8,9], chaotic dynamics [10,11], linear systems with additive disturbances [12], linear parameter-varying systems [13], etc. Assuming that a guaranteed bound of the initial unknown state and bounds on the uncertainties (inputs, disturbances, parameters, ...) are provided, a framer basically consists in an auxiliary dynamical system whose trajectories always stay above or below (component by component) those of the original system.…”

Sustainability and process control: A survey and perspective

“…Control for the corresponding photobioreactors has been targeted using PI control [180], input/output linearizing control [181,182], nonlinear output feedback control [183], passivity-based control [184], sliding mode control [185], adaptive control [186], linear MPC [187][188][189][190][191] and nonlinear MPC [192,193]. Lack of continuous online measurements has motivated the use of interval state estimation [194], moving horizon estimation [189] and extended Kalman filtering [182]. In order to tackle parametric uncertainly, a hierarchical control architecture has been proposed wherein a model predictive controller targets set point tracking and a sliding mode controller drives the system to the desired point by elimination of model-mismatch error [195].…”

Cardinality constrained robust optimization applied to a class of interval observers

“…We conduct a Monte Carlo analysis to characterize the performance improvement seen by using the proposed RIO (6) instead of the IO (2).…”

“…One of the earliest dynamical IOs was described in [1], where they were designed for a wastewater treatment management system. IOs have also been applied to population dynamics [1], algae cultures [2], and pharmacokinetics [3]. IOs are attractive in biotechnological applications due to the large parametric and measurement uncertainty inherent to biological systems.…”