Mathematical modeling is essential for understanding and controlling physical systems, particularly in scientific and engineering contexts. Accurate parameter estimation is critical for model reliability but often constrained by the cost and complexity of experiments. Optimal Experimental Design (OED) addresses this challenge by identifying experimental conditions that maximize information gain. Traditional OED approaches rely on the Fisher Information Matrix (FIM) and scalar optimality criteria, yet they are sensitive to unknown parameter values. To mitigate this, robust OED methods incorporate prior uncertainty, using strategies such as maximin and expectation-based criteria. In this work, we introduce a novel robust OED framework that unifies prior parameter uncertainty and measurement noise into an Overall Mean Squared estimation Error (OMSE) matrix. This formulation enables the use of standard optimality criteria while inherently accounting for both sources of uncertainty/noise. We demonstrate the effectiveness of our method through two case studies involving dynamical systems of varying complexity and discuss practical considerations for its implementation.

Upcycling residual streams generated by agri-food industries offers a promising strategy to reduce their environmental impact. In this context, biological conversion using purple non-sulfur bacteria (PNSB) is an attractive approach for valorizing organic residues. However, their dynamic modeling is still a recent area of interest, presenting numerous challenges related to observed behavior and sensitivity to operating conditions. This work investigated the dynamic modeling of PNSB growth cultivated on molasses under varying light intensities. A mechanistic model is first developed to predict biomass growth and carbon source consumption, while explicitly describing pH dynamics. The model (and its variants) is subsequently exploited under the paradigm of physics-informed neural networks (PINNs), and different PINN structures with varying levels of embedded physical knowledge are explored, including: (i) a PINN based on a physical model with explicit light intensity dependence, (ii) a PINN relying on a physical model without light dependence, (iii) a PINN trained combining structural physics with data-driven kinetics. In addition, a classical artificial neural network (ANN) trained with data augmentation is considered a purely data-driven benchmark. All approaches are evaluated for data fitting and predictive performance and compared with the proposed physical models. The results indicate that PINNs can improve predictive accuracy while preserving physical consistency, suggesting their potential for robust bioprocess modeling and as a basis for future control-oriented developments.

Thin-layer photobioreactors (TLRs) exhibit fast hydrodynamic and thermal dynamics, strong nonlinear photosynthetic responses and significant time-variability due to irradiance fluctuations and biomass growth. These characteristics challenge conventional model-based control strategies, whose tuning degrades under rapidly changing operating conditions. This work presents the experimental implementation of a model-free control approach, Extremum Seeking Control (ESC), for performance optimization in a semi-industrial thin-layer photobioreactor. Unlike previous studies in raceway ponds, the reduced hydraulic inertia of TLR systems enables the adaptation of this control strategy to accelerate convergence while preserving gradient estimation accuracy. The proposed approach is experimentally compared against classical on-off control and ESC configurations with and without feedforward compensation of solar irradiance. Beyond control performance metrics, biological indicators such as biomass concentration and productivity are evaluated to assess the impact on process efficiency. Results show that the proposed ESC strategy reduced cumulative CO_2 consumption by approximately 39

Optimal Experiment Design (OED) is an essential tool for selecting appropriate operating and sampling conditions for experimental runs that enable data collection for parameter estimation and model calibration. Based on an original Overall Mean Squared Error (OMSE) criterion recently proposed by the authors, which accounts for prior parameter uncertainty and measurement noise, this paper presents a MATLAB toolbox, OEDLab, that implements the method and its application to the identification of a HEK293 cell growth model. This case study highlights the selection of fed-batch input profiles and sampling schedules that minimize expected posterior uncertainty. Using Monte Carlo simulations with synthetic datasets generated with the OEDLab-optimal design, empirical parameter standard deviations align with root-mean-squared-error forecasts, and observed objective values mirror the predicted criteria.

Coordinating large swarms of unmanned aerial vehicles (UAVs) is a complex task due to high dimensionality and real-time computational demand. Effective formation control requires scalable strategies to maintain desired configurations while ensuring robustness to disturbances. This paper proposes a graph-based partitioning approach that divides the swarm into smaller, manageable subgroups, each of which is coordinated through an inter-partition communication network. This algorithm enables decentralized control, reducing computational complexity and enhancing scalability. This framework is integrated with a distributed control strategy, e.g., tube model predictive control, to ensure robust formation under uncertainties. Realistic simulations demonstrate the effectiveness of the proposed approach for UAV swarms.

This study reports on the development of a cascade control structure for a beer fermenter. The inner loop is based on a switched dynamic thermal model and a Kalman filter to estimate the heating (thermal resistor) and cooling (glycol cooler) power. Model predictive control (MPC) is used to track a temperature profile, which is provided by an outer loop that solves a multiobjective optimization problem. This latter task is achieved by a nonlinear model predictive controller based on an unscented Kalman filter estimating the unmeasured biological variables from a minimal number of online measurements, i.e., the flow of carbon dioxide and the density of the wort. The performance of the two control loops is demonstrated in several experiments at lab scale.

This work presents the implementation and experimental evaluation of an extremum seeking control (ESC) strategy for pH regulation in semi-industrial microalgae raceway photobioreactors, where pH is one of the most critical variables to control for ensuring stable and productive operation. A model-free optimization approach is proposed based on the classical modulation-demodulation ESC scheme, particularly suited to bioreactors whose dynamics evolve slowly and vary over time due to irradiance, temperature, mixing and biomass growth. To enable within-day convergence, the dither frequency was deliberately placed outside the dominant bandwidth of the process, ensuring sufficient excitation cycles during daylight operation. The high-pass filter (HPF) cutoff was then tuned to reject slow diurnal drifts while providing the phase lead required by the out-of-band design, thus preserving an accurate gradient estimate. In addition, a static data-driven feedforward of solar irradiance was incorporated to cancel predictable disturbances associated with photosynthetic activity, improving transient response and reducing corrective effort from the ESC loop. The approach was deployed on full-scale 80 m2 raceways under realistic outdoor and semi-industrial conditions. Results demonstrate robust pH regulation and fast daytime convergence toward the optimal operating region, with minimal modelling effort, highlighting ESC as a practical and effective tool for real-time pH control in microalgal bioprocesses.

This work investigates the use of extremum seeking control techniques for wind farm maximum power point tracking under uncertain and disturbed operating conditions. The study evaluates the robustness of extremumseeking strategies when applied to a representative wind farm layout inspired by a Belgian project. This efficient control strategy maximizes energy production without requiring an explicit physical model of the system by regulating the axial induction factors of the wind turbines to mitigate wake-induced losses. Classical and stabilizing extremum-seeking strategies are challenged to demonstrate the feasibility of maximum power point tracking within an extremum-seeking control framework. While both achieve satisfactory performance in dynamical and noise-free scenarios, only the stabilizing extremum-seeking technique exhibits robust performance in the presence of unexpected actuator dynamics and wind turbulence.

This paper evaluates the stability margin (SM) of heterogeneous ring vehicular networks containing a single distinct vehicle. While robustness analysis of string networks has been extensively studied using metrics such as L2-string stability and H infinity norms, ring networks-arising in closed traffic loops, satellite constellations, and circular autonomous formations-have received comparatively less attention. Moreover, existing studies of ring topologies typically assume homogeneous dynamics and do not provide general, analytically tractable robustness measures for heterogeneous systems. To address this gap, we characterize robustness using the minimum singular value (MSV) of the network transfer function. The main findings are threefold. First, two distinct SMs are introduced, which respectively quantify the allowable additive and multiplicative uncertainties that preserve closed-loop stability. Second, these margins admit compact characterizations in terms of vehicle parameters, revealing how heterogeneity in a single vehicle degrades network robustness. Third, tight analytical bounds on the SMs are derived by evaluating the frequency response of a scalar transfer function, avoiding the need to compute MSVs of large frequency-dependent matrices whose dimension grows with the number of vehicles. Numerical results demonstrate that the proposed SM captures robustness properties not revealed by H infinity- or string-stability-based metrics, highlighting its significance for heterogeneous ring networks.

Mathematical modeling has proven to be a highly effective tool for understanding microbial metabolism for which in-silico and experimental studies help to quantify intracellular mechanisms and pave the way for optimizing the production of molecules of interest. In that context, the development of metabolic networks turns out to be particularly interesting despite the challenges underlying their reconstruction. While the elaboration of genome-scale networks is computationally costly, small networks are often oversimplified and important biological mechanisms might be omitted, which limits their use in industrial applications. For this purpose, this study proposes a constructive bottom-up approach for the identification of metabolic networks of intermediate size, typically comprised of a couple of hundred reactions. It combines basic biological knowledge and a series of constraint-based methods in an iterative strategy, enabling the refinement of the network definition. The network is first validated using in-silico data, and subsequently refined using experimental data to enhance its biological relevance. Several case studies have been addressed to assess the efficiency of the methodology, and this paper focuses on the modeling of photosynthetic cyanobacteria Arthrospira sp. PCC 8005. The procedure is effective and provides promising results and metabolic analyses show consistent predictive capabilities of the network, in concordance with existing studies.

To match the growing demand for bio-methane production, anaerobic digesters need to embrace the co-digestion of different feedstocks; in addition, to improve the techno-economic performance, an optimal and time-varying adaptation of the input diet is required. These operation modes constitute a very hard challenge for the limited instrumentation and control equipment typically installed aboard full-scale plants. A model-based predictive approach may be able to handle such control problem, but the identification of reliable predictive models is limited by the low information content typical of the data available from full-scale plants' operations, which entail high parametric uncertainty. In this work, the application of a tube-based robust nonlinear model predictive control (NMPC) is proposed to regulate bio-methane production over a period of diet change in time, while warranting safe operation and dealing with uncertainties. In view of its upcoming validation on a true small pilot-scale plant, the NMPC capabilities are assessed via numerical simulations designed to resemble as much as possible the experimental setup, along with some practical final considerations.

Este trabajo presenta el diseño e implementación de una estrategia Extremum Seeking Control (ESC) aplicada a la regulación del pH en un raceway de microalgas. La dinámica del sistema presenta una constante de tiempo variable y muy lenta, lo que impide ubicar la señal de dither dentro del ancho de banda efectivo del sistema. Por ello, el dither se sitúa fuera de dicho ancho de banda, generando atenuación y desfase en la señal modulada. Para contrarrestar este efecto, se ajusta la frecuencia de corte de un filtro paso alto en la etapa de demodulación, de modo que el desfase total, resultado de la suma del desfase del sistema y el del filtro, se ubique aproximadamente en el centro del rango esperado. Esta estrategia mejora la robustez y estabilidad del ESC frente a las variaciones dinámicas del sistema. Además, se incorpora una acción feedforward para compensar perturbaciones medibles provocadas por la radiación incidente.

This article aims to tutorial a few important extremum seeking control approaches that can be used for the model-free optimization of industrial processes in various fields. The application of several methods is illustrated with a simple case study related to the production of algal biomass in photobioreactors. Other methods and applications are briefly reviewed.

Based on an available digital twin of a Vero cell culture process composed of a dynamic mechanistic model and a soft sensor, the impact of viral amplification is studied and optimized in the process development environment of Sanofi (Marcy l’Etoile, France). The soft sensor (an extended Kalman filter) uses Raman probe online measurements of biomass and some metabolites to estimate the infection titer and is combined with a model predictive controller that aims to optimize the infection titer while regulating the main substrate concentration level. The setup is validated in simulation, and a first experimental investigation is discussed.

Model-free extremum seeking (ES) has become a popular dynamic optimization strategy as it avoids the time-and resource-consuming task of developing a process model and identifying its parameters. This study explores the possibility of developing an ES control strategy for continuous cultures of micro-algae using minimum investment and, in particular, exploiting a simple "in-house" RGB sensor for biomass concentration. Besides the action on the dilution rate, variation in the incident light is also considered, and the lower sensitivity of the productivity with respect to this input is tackled by a Newton approach where the second-order information is inferred from an adaptive Hammerstein model included in the ES scheme. The setup is validated in simulation and experimental studies, demonstrating the strategy's good performance. Initialization is a critical factor to ensure fast convergence, and, to ensure robustness, bounds on the Hessian estimates have to be imposed.

The production of monoclonal antibodies (mAbs) is a complex pharmacological process involving upstream and downstream chains, focusing on mAbs production and purification, respectively. This paper presents a process optimization based on an end-to-end mechanistic model for the upstream process chain to enhance the production of mAbs. Upstream processing considers cell expansion, cell production, and primary harvesting steps by filtration. The optimization results offer users the optimal initial concentrations of the medium in the bioreactors, the duration of the cultures, the feed flow rate profiles, and the permeate flow profile in the filtration operation. Simulations incorporating interconnected reactors and process constraints led to optimized initial media concentrations and feed flow profiles, resulting in a 25% increase in mAb production compared to baseline conditions.

Extended Dynamic Mode Decomposition (EDMD) has received increasing attention in the last decade, but neural networks remain the most popular approach to the data-driven representation of biochemical processes in the published literature. This study explores the potential of pqEDMD a variant of EDMD using a reduced set of orthogonal polynomials to approximate the dynamics of a complex system, i.e., a raceway pond for the biological treatment of wastewater and the production of algal biomass. We carefully discuss the main ingredients of the method, and illustrate the performance of the method with numerical results, showing promising prospects. Copyright (c) 2025 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)

Collision avoidance is a problem largely studied in robotics, particularly in uncrewed aerial vehicle (UAV) applications. The main challenges in this area are hardware limitations, the need for rapid response, and the uncertainty associated with obstacle detection. Artificial potential functions (APOFs) are a prominent method to address these challenges. However, existing solutions lack assurances regarding closed-loop stability and may result in chattering effects. Hence, we propose a high-level control method for static obstacle avoidance based on multiple artificial potential functions (MAPOFs), with a set of switching rules with conditions on the parameter tuning ensuring the stability of the final position. The stability proof is established by analyzing the closed-loop system using tools from hybrid systems theory. Furthermore, we validate the performance of the MAPOF control through simulations and real-life experiments, showcasing its effectiveness in avoiding static obstacles.