This paper presents a deep learning framework for analyzing on-board vibration response signals in infrastructure health monitoring. The proposed WaveletInception–BiGRU network uses a Learnable Wavelet Packet Transform (LWPT) for early spectral feature extraction, followed by one-dimensional Inception-Residual Network (1D Inception-ResNet) modules for multi-scale, high-level feature learning. Bidirectional Gated Recurrent Unit (BiGRU) modules then integrate temporal dependencies and incorporate operational conditions, such as the measurement speed. This approach enables effective analysis of vibration signals recorded at varying speeds, eliminating the need for explicit signal preprocessing. The sequential estimation head further leverages bidirectional temporal information to produce an accurate, localized assessment of infrastructure health. Ultimately, the framework generates high-resolution health profiles spatially mapped to the physical layout of the infrastructure. Case studies involving track stiffness regression and transition zone classification using real-world measurements demonstrate that the proposed framework significantly outperforms state-of-the-art methods, underscoring its potential for accurate, localized, and automated on-board infrastructure health monitoring.

The partitioning problem is of central relevance for designing and implementing non-centralized Model Predictive Control (MPC) strategies for large-scale systems. These control approaches include decentralized MPC, distributed MPC, hierarchical MPC, and coalitional MPC. Partitioning a system for the application of non-centralized MPC consists of finding the best definition of the subsystems, and their allocation into groups for the definition of local controllers, to maximize the relevant performance indicators. The present survey proposes a novel systematization of the partitioning approaches in the literature in five main classes: optimization-based, algorithmic, community-detection-based, game-theoretic-oriented, and heuristic approaches. A unified graph-theoretical formalism, a mathematical re-formulation of the problem in terms of mixed-integer programming, the novel concepts of predictive partitioning and multi-topological representations, and a methodological formulation of quality metrics are developed to support the classification and further developments of the field. We analyze the different classes of partitioning techniques, and we present an overview of their strengths and limitations, which include a technical discussion about the different approaches. Representative case studies are discussed to illustrate the application of partitioning techniques for non-centralized MPC in various sectors, including power systems, water networks, wind farms, chemical processes, transportation systems, communication networks, industrial automation, smart buildings, and cyber–physical systems. An outlook of future challenges completes the survey.

This work analyzes how the trade-off between the modeling error, the terminal value function error, and the prediction horizon affects the performance of a nominal receding-horizon linear quadratic (LQ) controller. By developing a novel perturbation result of the Riccati difference equation, a novel performance upper bound is obtained and suggests that for many cases, the prediction horizon can be either 1 or +∞ to improve the control performance, depending on the relative difference between the modeling error and the terminal value function error. The result also shows that when an infinite horizon is desired, a finite prediction horizon that is larger than the controllability index can be sufficient for achieving a near-optimal performance, revealing a close relation between the prediction horizon and controllability. The obtained suboptimality performance upper bound is applied to provide novel sample complexity and regret guarantees for nominal receding-horizon LQ controllers in a learning-based setting. We show that an adaptive prediction horizon that increases as a logarithmic function of time is beneficial for regret minimization.

PieceWise Affine (PWA) approximations for nonlinear functions have been extensively used for tractable, computationally efficient control of nonlinear systems. However, reaching a desired approximation accuracy without prior information about the behavior of the nonlinear systems remains a challenge in the function approximation and control literature. As the name suggests, PWA approximation aims at approximating a nonlinear function or system by dividing the domain into multiple subregions where the nonlinear function or dynamics is approximated locally by an affine function also called local mode. Without prior knowledge of the form of the nonlinearity, the required number of modes, the locations of the subregions, and the local approximations need to be optimized simultaneously, which becomes highly complex for large-scale systems with multi-dimensional nonlinear functions. This paper introduces a novel approach for PWA approximation of multi-dimensional nonlinear systems, utilizing a hinging hyperplane formalism for cut-based partitioning of the domain. The complexity of the PWA approximation is iteratively increased until reaching the desired accuracy level. Further, the tractable cut definitions allow for different forms of subregions, as well as the ability to impose continuity constraints on the PWA approximation. The methodology is explained via multiple examples and its performance is compared to two existing approaches through case studies, showcasing its efficacy.

This paper presents a novel distributed model predictive control (MPC) formulation without terminal cost and a corresponding distributed synthesis approach for distributed linear discrete-time systems with coupled constraints. The proposed control scheme introduces an explicit stability condition as an additional constraint based on relaxed dynamic programming. As a result, contrary to other related approaches, system stability with the developed controller does not rely on designing a terminal cost. A distributed synthesis approach is then introduced to handle the stability constraint locally within each local agent. To solve the underlying optimization problem for distributed MPC, a violation-free distributed optimization approach is developed, using constraint tightening to ensure feasibility throughout iterations. A numerical example demonstrates that the proposed distributed MPC approach ensures closed-loop stability for each feasible control sequence, with each agent computing its control input in parallel.

Dispersion modeling is crucial for marine environmental modeling and management. However, operational applications require a practical balance between model accuracy and computational efficiency. To address this challenge, we develop and validate a generalized cell-based model (CBM) framework for contaminant dispersion. The framework enhances physical realism through a novel three-dimensional (3D) transport model and a formulation for chemical reactions. Additionally, a new discretization-based approach is proposed to robustly relate the CBM’s diffusion coefficient to its partial differential equation counterpart, improving performance in scenarios with sharp gradients of the concentration level. The proposed framework’s favorable trade-off between accuracy and efficiency is demonstrated in a comparative simulation study, where the 3D CBM reduces computation time from 14.72 s to 0.06 s compared to finite-element methods (FEM), with a relative Root Mean Square Error (RMSE) of 7.67%. To demonstrate its practical applicability, the proposed framework is validated using ocean current and nitrate concentration data from the Copernicus Marine Environment Monitoring Service. After identifying a key model parameter from the data, the model’s forward predictions accurately reproduce the observed nitrate concentration patterns, confirming its suitability for operational scenarios.

Learning-based control with safety guarantees usually requires real-time safety certification and modifications of possibly unsafe learning-based policies. The control barrier function (CBF) method uses a safety filter (SF) containing a constrained optimization problem to produce safe policies. However, finding a valid CBF for a general nonlinear system requires a complex function parameterization, which in general makes the policy optimization problem difficult to solve in real time. For nonlinear systems with nonlinear state constraints, this paper proposes the novel concept of state-action CBFs (SACBFs), which do not only characterize the safety at each state but also evaluate the control inputs taken at each state. SACBFs, in contrast to CBFs, enable a flexible parameterization, resulting in a SF that involves a convex quadratic optimization problem, which significantly alleviates the online computational burden. We propose a learning-based approach to synthesize SACBFs. The effect of learning errors on the effectiveness of SACBFs is addressed by constraint tightening and introducing a new concept called contractive-set CBFs. This ensures formal safety guarantees for the learned CBFs and control policies. Simulation results on an inverted pendulum with elastic walls validate the proposed CBFs in terms of constraint satisfaction and CPU time.

Marine litter pollution is a major environmental threat due to the widespread presence of plastics and their detrimental impact on marine life and human health. There is a need for autonomous systems with computer vision to help clean the oceans. This study compares the latest state-of-the-art You Only Look Once (YOLO) models YOLOv9 - YOLOv12 in an underwater object detection setting in terms of accuracy, computational speed, and architecture complexity. We specifically focus on the smallest versions of these architectures, due to the real-time constraints of the setting. Multiple underwater datasets are combined to obtain a wide representation of underwater conditions and marine objects. The findings provide valuable insights into selecting and optimizing object detection architectures for underwater litter detection, contributing to monitoring marine ecosystems and addressing marine pollution. This work can be used as a building ground for further improving underwater object detection systems.

Greenhouse climate control is concerned with maximizing performance in terms of crop yield and resource efficiency. One promising approach is model predictive control (MPC), which leverages a model of the system to optimize the control inputs, while enforcing physical constraints. However, prediction models for greenhouse systems are inherently inaccurate due to the complexity of the real system and the uncertainty in predicted weather profiles. For model-based control approaches such as MPC, this can degrade performance and lead to constraint violations. Existing approaches address uncertainty in the prediction model with robust or stochastic MPC methodology; however, these necessarily reduce crop yield due to conservatism and often bear higher computational loads. In contrast, learning-based control approaches, such as reinforcement learning (RL), can handle uncertainty naturally by leveraging data to improve performance. This work proposes an MPC-based RL control framework to optimize the climate control performance in the presence of prediction uncertainty. The approach employs a parametrized MPC scheme that learns directly from data, in an online fashion, the parametrization of the constraints, prediction model, and optimization cost that minimizes constraint violations and maximizes climate control performance. Simulations show that the approach can learn an MPC controller that significantly outperforms the current state-of-the-art in terms of constraint violations and efficient crop growth.

Temperature plays a critical role in performance and stability of anaerobic digestion processes, subject to frequent meteorological fluctuations. However, state-of-the-art modeling and process control approaches for anaerobic digestion often do not consider the temporal dynamics of the temperature, which can influence microbial communities, kinetics, and chemical equilibrium, and consequently, biogas production efficiency. Therefore, to account for anaerobic digesters operating under fluctuating meteorological conditions, the Anaerobic Digestion Model no. 1 (ADM1) is mechanistically extended in this paper to incorporate temporal changes into temperature-dependent parameters by defining inhibition functions for microbial activities using the cardinal temperature model, and accounting for the lag in microbial adaptation to temperature fluctuations using a time-lag adaptation function. Thereafter, given that temperature fluctuations are a significant disturbance, a control framework based on Model Predictive Control (MPC) is developed to regulate the feeding flow rate and to ensure stable production rates despite temperature disturbances without relying on direct temperature control. An adaptive MPC approach is formulated based on a linear input–output model, where the parameters of the linear model are updated online to capture the nonlinear dynamics of the process and frequent changes in the dynamics accurately. In addition, a fuzzy logic system is employed to assign a reference trajectory for the production rate based on the temperature and its rate of change. Integrating this fuzzy logic system with the MPC controller enhances the production rate on warm days and avoids the operational failure in production on cold days. Additionally, to enhance biogas production rates, the feasibility of utilizing a portion of the produced biogas for external heating purposes is also investigated. It is demonstrated that by utilizing the proposed MPC approach, the additional amount of feed for the digester to produce methane required for a self-consumption biogas-fueled heating system can be calculated according to the meteorological variations. This enhances the process performance and stability. Finally, a thermally optimized dome digester semi-buried in the ground, operating under climate conditions of The Netherlands is considered as a case study to validate the extended model in agreement with biological and physicochemical behaviors of real-world applications, and to demonstrate the effectiveness of the proposed control system in handling temperature changes and enhancing performance.

Infinite-horizon optimal control of constrained piecewise affine (PWA) systems has been approximately addressed by hybrid model predictive control (MPC), which, however, has computational limitations, both in offline design and online implementation. In this article, we consider an alternative approach based on approximate dynamic programming (ADP), an important class of methods in reinforcement learning. We accommodate nonconvex union-of-polyhedra state constraints and linear input constraints into ADP by designing PWA penalty functions. PWA function approximation is used, which allows for a mixed-integer encoding to implement ADP. The main advantage of the proposed ADP method is its online computational efficiency. Particularly, we propose two control policies, which lead to solving a smaller-scale mixed-integer linear program than conventional hybrid MPC, or a single convex quadratic program, depending on whether the policy is implicitly determined online or explicitly computed offline. We characterize the stability and safety properties of the closed-loop systems, as well as the suboptimality of the proposed policies, by quantifying the approximation errors of value functions and policies. We also develop an offline mixed-integer-linear-programming-based method to certify the reliability of the proposed method. Simulation results on an inverted pendulum with elastic walls and on an adaptive cruise control problem validate the control performance in terms of constraint satisfaction and CPU time.

The European Economic Area Electricity Network Benchmark (EEA-ENB) is a multi-area power system representing the European network of transmission systems for electricity to facilitate the application of distributed control techniques. In the EEA-ENB, we consider the Load Frequency Control (LFC) problem in the presence of Renewable Energy Sources (RESs), and Energy Storage Systems (ESSs). RESs are known to cause instability in power networks due to their inertialess and intermittent characteristics, while ESSs are introduced as a resource to mitigate the problem. In the EEA-ENB, particular attention is dedicated to Distributed Model Predictive Control (DMPC), whose application is often limited to small and homogeneous test cases due to the lack of standardized large-scale scenarios for testing, and due to the large computation time required to obtain a centralized MPC action for performance comparison with DMPC strategies under consideration. The second problem is exacerbated when the scale of the system grows. To address these challenges and to provide a real-world-based and control-independent benchmark, the EEA-ENB has been developed. The benchmark includes a centralized MPC strategy providing performance and computation time metrics to compare distributed control within a repeatable and realistic simulation environment.

In this chapter, we explore model predictive control of fuel cell electric vehicles (FCEVs), a type of vehicle that utilizes the chemical energy of hydrogen to generate electricity for their power train. Since vehicles are typically utilized for mobility purposes only for a fraction of the time, the energy stored in the onboard hydrogen tanks of these vehicles also can be used to supply power when they are parked. Our focus is on examining how to control the operation of FCEVs, ensuring the fulfilment of constraints imposed by both electrical and transportation networks while minimizing operational costs.

Maintenance is a necessary to keep assets, in this case, a pavement system, in good condition. Spending too much on maintenance is not efficient, while not spending enough may cause the condition to drop below a desired level. Therefore, in this paper, a conceptual approach, based on systems and control theory, is developed to improve the efficiency of maintenance of a pavement system, compared to the currently used maintenance approach where often only fixed bounds of the condition determine whether or not a maintenance action is required.  A state-space description of the condition of the pavement system is chosen for predicting the future evolution of the health condition. This allows the use of a moving-horizon optimisation approach, to determine optimal anticipative maintenance actions. Furthermore, in this approach, the maintenance cost and the condition of the pavement system are optimised. This model-based approach can be applied in practice as well-documented data, from which degradation models can be constructed, are often available. In this paper, we also show how degradation models from the literature can be converted for use in the proposed condition-based maintenance approach. Note that because of the general character of the proposed maintenance optimisation approach, the degradation model and the chosen optimisation method that are used as illustration in this paper can easily be replaced by another one, depending on the needs of the user. A case study is performed, where a representative situation is considered using the developed approach and the maintenance approach currently used in practice. This case study shows how the approach works and what the cost reduction can be assuming that the models are accurate. The paper ends with a discussion and recommendations.

The growing volume of available infrastructural monitoring data enables the development of powerful data-driven approaches to estimate infrastructure health conditions using direct measurements. This paper proposes a deep learning methodology to estimate infrastructure physical parameters, such as railway track stiffness, using drive-by vibration response signals. The proposed method employs a long short-term memory (LSTM) feature extractor accounting for temporal dependencies in the feature extraction phase, and bidirectional long short-term memory (BiLSTM) networks to leverage bidirectional temporal dependencies in both the forward and backward paths of the drive-by vibration response in the condition estimation phase. In addition, a framing approach is employed to enhance the resolution of the monitoring task to the beam level by segmenting the vibration signal into frames equal to the distance between individual beams, centering the frames over the beam nodes. The proposed LSTM-BiLSTM model offers a versatile tool for various bridge and railway infrastructure conditions monitoring using direct drive-by vibration response measurements. The results demonstrate the potential of incorporating temporal analysis in the feature extraction phase and emphasize the pivotal role of bidirectional temporal information in infrastructure health condition estimation. The proposed methodology can accurately and automatically estimate railway track stiffness and identify local stiffness reductions in the presence of noise using drive-by measurements. An illustrative case study of vehicle–track interaction simulation is used to demonstrate the performance of the proposed model, achieving maximum mean absolute percentage errors of 1.7% and 0.7% in estimating railpad and ballast stiffness, respectively.

Implementing model predictive control (MPC) in practice faces many subtle but prevalent problems, including modeling errors, solver errors, and actuator faults. In essence, the real control input applied to the system always deviates from the ideal one based on a perfect controller, resulting in an imperfect controller. In this letter, we provide a general analysis to quantify the suboptimality of MPC for Lipschitz-continuous nonlinear systems due to imperfect control inputs in terms of dynamic regret. Based on a general assumption about how the imperfect controller may improve over time, sublinear regret upper bounds are established for cases where the closed-loop system under the ideal controller is Lipschitz-contractive (i.e., its Lipschitz constant is smaller than one). In addition, we also discuss how the regret scales when the closed-loop system under the oracle controller is not Lipschitz-contractive. The results provide insights into designing suitable MPC strategies, especially for learning-based MPC.